You appear to have several questions wrapped into one. Let's consider them one at a time.
Regarding the Bible Sabbath
The Bible follows the Hebrew tradition and focus of the weekly Sabbath, the birthday of the world and the day of rest as commanded by God, as the highlight of each week. None of the other days were given names. In Hebrew, one would always count those days by their number--toward the seventh-day Sabbath. The Sabbath was the only day of the week with a name. Certain festival days, like Passover, were given names as well, but these also became ceremonial sabbaths, even when they did not coincide with the weekly Sabbath. When a ceremonial sabbath landed on a weekly Sabbath, it was considered a high Sabbath.
Regarding Calendar Changes
Not once has the weekly cycle been interrupted by any of the changes made to the calendar. In transitioning from the Julian Calendar, to the Gregorian Calendar, for example, ten days were dropped out, going from October 4 to October 15 on the next weekly day, whereas the week had no change at all, only the dates changed. Similarly, time changes are made so as to be past the point of making a date change, i.e. there is no shift from Sunday to Monday, or vice versa, during a time change.
Translators often choose to interpret instead of translate, and this can be for a variety of reasons. Sometimes it is necessary, such as when a word or concept does not exist in the target language. But it is often more suitable for a Bible commentary where an explanation can be given. For example, when Jesus is said to have died "at the ninth hour," this follows the Greek schedule of beginning the day at 6 a.m. The ninth hour would be three o'clock in the afternoon--and some translations convert between those two times, potentially destroying the significance (if it has any) to the number "nine" which was present in the original text, favoring a more "understandable" rendering.
I'm not aware of translations using names of weekdays like "Friday," but this obviously would exceed the proper bounds of translation every bit as much as the KJV's embarrassing insertion of "Easter" in place of "Passover" in Acts 12:4.
The Sabbath, and the weekly cycle, is sure, and has never been changed. Careful study of the historical changes made to the calendar will bear this out. Translations, on the other hand, are frequently subjective: reader beware.