"She is the subject of preaching and worship" Mary worship?

This meme has been circulating among some Protestant polemicists who go after Catholicism.

"Having entered deeply into the history of salvation, Mary, in a way, unites in her person and re-echoes the most important doctrines of the faith: and when she is the subject of preaching and worship she prompts the faithful to come to her Son, to his sacrifice and to the love of the Father."--Vatical Council II, Official Teachings of Roman Catholicism Vol. 1, pg. 420 and 421 

This article will deal with the first quote.

Like all good social media polemics, its fully of typos and poor references. Obviously, it is supposed to read "Vatican II." The citation is nonsense, probably is supposed to be a book on Vatican II. Regardless, it is taken from Lumen Gentium 65 of Vatican II. The translation I have only found on the Legion of Mary's website, retaining the archaic usage of worship. As I mentioned elsewhere, even Protestants in older English used the word worship in a broader sense which could be titles of justices, mayors etc, eg the Worshipful Smith.

The translation the Vatican's website has reads:

But while in the most holy Virgin the Church has already reached that perfection whereby she is without spot or wrinkle, the followers of Christ still strive to increase in holiness by conquering sin.(Cf. Eph 5, 27.) And so they turn their eyes to Mary who shines forth to the whole community of the elect as the model of virtues. Piously meditating on her and contemplating her in the light of the Word made man, the Church with reverence enters more intimately into the great mystery of the Incarnation and becomes more and more like her Spouse. For Mary, who since her entry into salvation history unites in herself and re-echoes the greatest teachings of the faith as she is proclaimed and venerated, calls the faithful to her Son and His sacrifice and to the love of the Father. Seeking after the glory of Christ, the Church becomes more like her exalted Type, and continually progresses in faith, hope and charity, seeking and doing the will of God in all things. Hence the Church, in her apostolic work also, justly looks to her, who, conceived of the Holy Spirit, brought forth Christ, who was born of the Virgin that through the Church He may be born and may increase in the hearts of the faithful also. The Virgin in her own life lived an example of that maternal love, by which it behooves that all should be animated who cooperate in the apostolic mission of the Church for the regeneration of men.--Vatican II, Lumen Gentium 65. (translation per the Vatican website)

The official Latin text is :

Dum autem Ecclesia in Beatissima Virgine ad perfectionem iam pertingit, qua sine macula et ruga existit (cf. Eph 5,27), christifideles adhuc nituntur, ut devincentes peccatum in sanctitate crescant; ideoque oculos suos ad Mariam attollunt, quae toti electorum communitati tamquam exemplar virtutum praefulget. Ecclesia de Ea pie recogitans Eamque in lumine Verbi hominis facti contemplans, in summum incarnationis mysterium venerabunda penitius intrat, Sponsoque suo magis magisque conformatur. Maria enim, quae, in historiam salutis intime ingressa, maxima fidei placita in se quodammodo unit et reverberat, dum praedicatur et colitur, ad Filium suum Eiusque sacrificium atque ad amorem Patris credentes advocat. Ecclesia vero, gloriam Christi prosequens, praecelso suo Typo similior efficitur, continuo progrediens in fide, spe et caritate, ac divinam voluntatem in omnibus quaerens et obsequens. Unde etiam in opere suo apostolico Ecclesia ad Eam merito respicit, quae genuit Christum, ideo de Spiritu Sancto conceptum et de Virgine natum, ut per Ecclesiam in cordibus quoque fidelium nascatur et crescat. Quae Virgo in sua vita exemplum exstitit materni illius affectus, quo cuncti in missione apostolica Ecclesiae cooperantes ad regenerandos homines animentur oportet.--Vatican II, Lumen Gentium 65

The Latin word in question is "colitur" which the Vatican's site reads as "venerated." 

This is not the ordinary word for worship, the word used literally means to cultivate (a field).

It sometimes is used for worship of God, or giving honor to someone else.

Wiktionary defines it as:

colō (present infinitive colere, perfect active coluī, supine cultum); third conjugation 

to cultivate the land, till, tend, take care of a field or garden (literal)

Synonyms: incolō, subigō 

to inhabit

Synonyms: habitō, obsideō, resideō, possideō, cōnsīdō, iaceō, subsīdō, stabulō, incolō, vīvō, versor 

to frequent, be the guardian of, cherish, care for, protect, nurture

Synonyms: cūrō, accūrō, prōcūrō, videō, respiciō, cōnsultō, cōnsulō, caveō, serviō 

(figuratively) to worship, honor, revere, reverence --https://en.wiktionary.org/wiki/colo#Latin

The same entry provides the declensions which includes the nominative, masculine which is cultus, the word used for devotions to saints. 

A more formal dictionary, provide a very broad definition, it reads:

COL-, to till, tend, care for, cultivate: agrum, T.: agros, Cs.: colendi causā in agro esse: agri qui coluntur: hortos, V.: arbores, H.: fructūs, V.: fruges, O.: Pater ipse colendi, V.—To frequent, dwell in, stay in, inhabit, abide, live, dwell: colitur ea pars (urbis): urbem, V.: regnum, O.: arva gelidumque Anienem, and the banks of, V.: Rheni ripam, Ta.: anguis Stagna colit, haunts, V.: proximi Cattis Usipii colunt, Ta.: circa ripam Rhodani, L.—Fig., of the gods, to frequent, cherish, care for, protect, guard, watch over: quas condidit arces, Ipsa colat, V.: nymphis colentibus undas, O.: Iuno, quae Veios colis, L.: urbem, L.: terras hominumque genus, H. — To honor, revere, reverence, worship: Mercurium, Cs.: deos patrios: Musarum delubra: sacra: o colendi Semper et culti, H.: colebantur religiones pie, L.: numina, V.: caerimonias sepulcrorum: sacrarium summā caerimoniā, N. — To honor, esteem, love, adhere to, cherish: nos coluit maxime, T.: a quibus diligenter videmur coli: hunc virum, S.: poëtarum nomen: in amicis colendis: plebem Romanam, L.: alqm litteris, N.: nec illos arte, nec opulenter, S.—To attend to, dress, clothe, adorn, etc.: formamque augere colendo, by attire, O.—To cultivate, cherish, seek, practise, devote oneself to, follow, observe: studia: fidem rectumque, O.: ius et fas, L.: memoriam alicuius: bonos mores, S.: pietatem, T.: ius bonumque, S.: orationis genus: patrias artes, O.—To experience, live through, pass, spend: vitam illam: vitam inopem, T. -- Lewis, Charlton, T. An Elementary Latin Dictionary. New York, Cincinnati, and Chicago. American Book Company. 1890. Entry for Colo

The same Vatican II document cited (Lumen Genitum) does not regard colitur as interchangable with adoration, and actually clarifies the matter, this is the VERY next paragraph after the one cited in the OP with Latin in parenthesis:

Clearly from earliest times the Blessed Virgin is honored (colitur) under the title of Mother of God, under whose protection the faithful took refuge in all their dangers and necessities. [(21*) Sub tuum praesidium] Hence after the Synod of Ephesus the cult of the people of God toward Mary wonderfully increased in veneration and love (veneratione et dilectione), in invocation and imitation, according to her own prophetic words: “All generations shall call me blessed, because He that is mighty hath done great things to me”. (Lk. 1, 48.) This cult (cultus), as it always existed, although it is altogether singular, differs essentially from the cult of adoration (adorationis) which is offered to the Incarnate Word, as well to the Father and the Holy Spirit, and it is most favorable to it. --Vatican II, Lumen Gentium 66. (translation per the Vatican website)

The official Latin text reads: 

 Maria, per gratiam Dei post Filium prae omnibus angelis et hominibus exaltata, utpote sanctissima Dei Mater, quae mysteriis Christi interfuit, speciali cultu ab Ecclesia merito honoratur. Et sane ab antiquissimis temporibus Beata Virgo sub titulo "Deiparae" colitur, sub cuius praesidium fideles in cunctis periculis et necessitatibus suis deprecantes confugiunt(191). Inde praesertim ab Ephesina Synodo cultus Populi Dei erga Mariam mirabiliter crevit in veneratione et dilectione, in invocatione et imitatione, secundum ipsius verba prophetica: "Beatam me dicent omnes generationes, quia fecit mihi magna qui potens est" (Lc 1,48-49). Qui cultus, prout in Ecclesia semper exstitit, singularis omnino quamquam est, essentialiter differt a cultu adorationis, qui Verbo incarnato aeque ac Patri et Spiritui Sancto exhibetur, eidemque potissimum favet. Variae enim formae pietatis erga Dei Genitricem, quas Ecclesia intra limites sanae et orthodoxae doctrinae, pro temporum et locorum conditionibus et pro indole ingenioque fidelium approbavit, id efficiunt ut dum Mater honoratur, Filius, propter quem omnia (cf. Col 1,15-16) et in quo aeterno Patri "complacuit omnem plenitudinem inhabitare" (Col 1,19), rite noscatur, ametur, glorificetur, Eiusque mandata serventur.--Vatican II, Lumen Gentium 66

Another instance is modern Ecclesiastical Latin, is the Papal Encyclical by Pope John Paul II:

Vera libertas non est ubi vita non colitur et diligitur; neque plena est vita nisi in libertate.--Evangelium Vitae 96

There is no true freedom where life is not welcomed and loved; and there is no fullness of life except in freedom.--Evangelium Vitae 96

Also, John Paul II produced an Apostolic Letter called Maxime Colitur "Highest Veneration," which starts as:

Ad perpetuam rei memoriam. – Maxime colitur a populo christiano Deipara Maria, «quae signum sacrae virginitatis extulit, et intemeratae integritatis pium Christo vexillum erexit» (S. Ambrosius, De institutione Virginis, V).--Pope John Paul II, Apostolic Letter, Maxime Coliter (Official Latin Vatican text)

My informal translation: 

For a perpetual record of the matter--Mary, the mother of God, is most venerated by the Christian people, "she who raised up the sign (signum) of sacred virginity and lifted up the pious standard (vexillum) of undefiled integrity for Christ" (St. Ambrose, An Instruction for a Virgin, 5).--Pope John Paul II, Apostolic Letter, Maxime Coliter

John Paul seemed to be quite fond of using this word.

For its appearance in older Latin.

To be continued...