Sunday, Sabbath, first of the week

The Scriptures tells us a few times that the early apostolic church gathered for "breaking bread" ie the Mass, on the first day of the week, which refers to Sunday.

On the first day of the week, when we were gathered together to break bread, Paul talked with them, intending to depart on the morrow; and he prolonged his speech until midnight.--Acts 20:7 RSV

On the first day of every week, each of you is to put something aside and store it up, as he may prosper, so that contributions need not be made when I come. --1 Corinthians 16:2 RSV

Since, this can be problematic for groups with Judaizing, Sabbath-keeping urges like the Seventh Day Adventists, Seventh Day Baptists and other Sabbath keeping Christian sects, some of their apologists insist these verses are actually about the Sabbath, since it has the Greek word sabbaton, which is sabbaths. As seen here:

Ἐν δὲ τῇ μιᾷ τῶν σαββάτων, συνηγμένων τῶν μαθητῶν κλάσαι ἄρτον, ὁ Παῦλος διελέγετο αὐτοῖς, μέλλων ἐξιέναι τῇ ἐπαύριον, παρέτεινέν τε τὸν λόγον μέχρι μεσονυκτίου. --Acts 20:7 Byzantine Majority text (the non Byzantine manuscript are the same except replace τῶν μαθητῶν with ἡμῶν)

Κατὰ μίαν σαββάτων ἕκαστος ὑμῶν παρ' ἑαυτῷ τιθέτω, θησαυρίζων ὅ τι ἂν εὐοδῶται, ἵνα μή, ὅταν ἔλθω, τότε λογίαι γίνωνται. --1Corinthians 16:2 (Byzantine text, other texts vary in spelling had read 'sabbatou')

So the rebuttal boils down to "see this is actually taking place on the Sabbath, it doesn't say 'week.' At first, this rebuttal seemed impressive, until other verses with the same words are inspected that use sabbaton (said savvaton actually). We can look through the Gospel accounts see the phrase "first of the Sabbaths" (μίαν σαββάτων or,πρώτῃ σαββάτου) is translated as "first day of the week":

Now after the sabbath, toward the dawn of the first day of the week, Mary Mag′dalene and the other Mary went to see the sepulcher.--Matthew 28:1 RSV

Ὀψὲ δὲ σαββάτων, τῇ ἐπιφωσκούσῃ εἰς μίαν σαββάτων, ἦλθεν Μαρία ἡ Μαγδαληνή, καὶ ἡ ἄλλη Μαρία, θεωρῆσαι τὸν τάφον.--Matthew 28:1 RSV

And when the sabbath was past, Mary Mag′dalene, and Mary the mother of James, and Salo′me, bought spices, so that they might go and anoint him.  And very early on the first day of the week they went to the tomb when the sun had risen.--Mark 16:1-2 RSV

Καὶ διαγενομένου τοῦ σαββάτου, Μαρία ἡ Μαγδαληνὴ καὶ Μαρία Ἰακώβου καὶ Σαλώμη ἠγόρασαν ἀρώματα, ἵνα ἐλθοῦσαι ἀλείψωσιν αὐτόν.  Καὶ λίαν πρωῒ τῆς μιᾶς σαββάτων ἔρχονται ἐπὶ τὸ μνημεῖον, ἀνατείλαντος τοῦ ἡλίου. --Mark 16:1-2 Byzantine Text 

Now when he rose early on the first day of the week, he appeared first to Mary Mag′dalene, from whom he had cast out seven demons--Mark 16:9

Ἀναστὰς δὲ πρωῒ πρώτῃ σαββάτου ἐφάνη πρῶτον Μαρίᾳ τῇ Μαγδαληνῇ, ἀφ' ἧς ἐκβεβλήκει ἑπτὰ δαιμόνια. --Mark 16:9 (Byzantine Text)  

But on the first day of the week, at early dawn, they went to the tomb, taking the spices which they had prepared.--Luke 24:1 

Τῇ δὲ μιᾷ τῶν σαββάτων, ὄρθρου βαθέος, ἦλθον ἐπὶ τὸ μνῆμα, φέρουσαι ἃ ἡτοίμασαν ἀρώματα, καί τινες σὺν αὐταῖς. --Luke 24:1 Byzantine Text (other texts omit ἦλθον and καί τινες σὺν αὐταῖς)

Now on the first day of the week Mary Mag′dalene came to the tomb early, while it was still dark, and saw that the stone had been taken away from the tomb.--John 20:1 RSV

Τῇ δὲ μιᾷ τῶν σαββάτων Μαρία ἡ Μαγδαληνὴ ἔρχεται πρωΐ, σκοτίας ἔτι οὔσης, εἰς τὸ μνημεῖον, καὶ βλέπει τὸν λίθον ἠρμένον ἐκ τοῦ μνημείου.--John 20:1 (all major texts)

On the evening of that day, the first day of the week, the doors being shut where the disciples were, for fear of the Jews, Jesus came and stood among them and said to them, “Peace be with you.”--John 20:19

Οὔσης οὖν ὀψίας, τῇ ἡμέρᾳ ἐκείνῃ τῇ μιᾷ τῶν σαββάτων, καὶ τῶν θυρῶν κεκλεισμένων ὅπου ἦσαν οἱ μαθηταὶ συνηγμένοι, διὰ τὸν φόβον τῶν Ἰουδαίων, ἦλθεν ὁ Ἰησοῦς καὶ ἔστη εἰς τὸ μέσον, καὶ λέγει αὐτοῖς, Εἰρήνη ὑμῖν. --John 20:19 (Byzantine Majority, over texts omit "τῶν" (the) before σαββάτων, and συνηγμένοι (assembled).

Since Christ rose on a Sunday and rested in the tomb on the Sabbath, these women were not coming on the Sabbath day since Christ has risen by this time.

We read in Luke's account that the Pharisees fasted twice a "week":

I fast twice a week, I give tithes of all that I get.’--Luke 18:12

The Greek reads in the place of "week"--sabbatou.

 Νηστεύω δὶς τοῦ σαββάτου, ἀποδεκατῶ πάντα ὅσα κτῶμαι. --Luke 18:12

Pharisees fasted "twice" on a Sabbath? or twice a week? The Jewish custom was to fast on Monday and Thursday--not two times on the same day.

From my search it appears that the Greek word for "week" as used in the LXX is not used in the NT. The LXX uses the word ἑβδομάδας for a period of seven, as in Daniel 10:2

ἐν ταῖς ἡμέραις ἐκείναις ἐγὼ Δανιηλ ἤμην πενθῶν τρεῖς ἑβδομάδας ἡμερῶν--Daniel 10:2 LXX

In those days I, Daniel, was in mourning for three weeks of days.--Daniel 10:2 NET

Hebrew of Daniel 10:2-- בַּיָּמִים, הָהֵם--אֲנִי דָנִיֵּאל הָיִיתִי מִתְאַבֵּל, שְׁלֹשָׁה שָׁבֻעִים יָמִים

The Daniel Text in both Hebrew and Greek use a words proper to those languages for a week---"seven days."

 Every time any translation of the NT uses the word "week" the word is always some form of "sabbaton."

The New Testament uses the same term for Sunday as found in Jewish literature of the first millennium, for instance in the Babylonian Talmud Tannit 29b its read:

חל להיות באחד בשבת מותר לכבס כל השבת כולה
בשני בשלישי ברביעי ובחמישי לפניו אסור לאחריו מותר חל להיות בערב שבת מותר לכבס בחמישי מפני כבוד השבת 

תלמוד בבלי, מסכת תענית פרק ד כט,ב גמרא

Should it fall on Sunday (באחד בשבת b'echad b'shavat-- in one [of] shavat/sabbath) it is permissible to wash clothes the whole of the week ( השבת hashshavat--the Sabbath/week), [but should it fall] on Monday or Tuesday or Wednesday or Thursday, before it it is not permissible, but after it, it is permissible;[should it fall] on Friday it is permissible to wash clothes on Thursday in honour of the Sabbath--Mas. Ta'anit 29b (page 94), Babylonian Talmud, Seder Mo'ed

The sentence חל להיות באחד בשבת מותר לכבס כל השבת כולה is translated as "Should it fall on Sunday it is permissible to wash clothes the whole of the week." באחד is "b'echad" that is "In/on One" and בשבת is "on Sabbath/week," here it means "week" and is translated as week. Then at the end the word shavat is used again, "kal hashshavat " meaning either "whole Sabbath" or "whole week" and obviously Jews are not to wash clothes on the Sabbath day. Translators of the Talmud translate the phrase "one of/in Sabbath" as "Sunday" just as the New Testament has always been understood. So,

μίαν σαββάτων in the Greek New Testament is the equal of the Hebrew Talmudic phrase באחד בשבת . Where both texts read "one of the Sabbath(s)" to refer to Sunday, which is modern Hebrew is Yom Rishon.

On this matter, John Lightfoot, a commentator and scholar on Judaism said:

εἰς μίαν σαββάτων " Towards the first day of the week."] The Jews reckon the days of the week thus; באחד בשבת "One day" (or the first day) "of the Sabbath:"  תרי בשבא "two" (or the second day) "of the Sabbath:"--"Two witnesses come and say, בחד בשבא The first of the Sabbath, this man stole, &c ובתרי בשבא and, on the second day of the Sabbath, judgment passed on him."--"The whole works of Rev. John Lightfoot, D.D., Volume XI, Exercitations upon the Gospel of St. Matthew, Chapter XVIII:1, page 357)