As far as the sabbath is concerned this was not re stated and in fact mentions that it no longer applied.
Lets go back to the old testament first
Exodus 31:16,17 speaks of God telling the Israelites to observe a Sabbath (which is a day of rest and worship to him) that it was a indefinite covenant between them. Indefinite doesn’t always mean forever but rather the definition of the word means ‘Lasting for an unknown length of time’.
The Hebrew word used here ‘oh lam’ that’s translated to the English indefinite actually means ‘a period of time’, not a permanent covenant but some bibles have translated it as a ‘perpetual covenant’ perpetual meaning ‘never ending’ so its important that the correct meaning of oh lam is used. So the Sabbath was for the nation of Israel for a set time and was not an ongoing obligation for everyone else.
Interestingly, I found that The same word (Oh lam) is used at Numbers 25:13 in relation to the priesthood which later ended according to Hebrews 7:12.
Lets now look at the new teatament
Colossians 2:13-16 - "Furthermore, though YOU were dead in YOUR trespasses and in the uncircumcised state of YOUR flesh, [God] made YOU alive together with him. He kindly forgave us all our trespasses and blotted out the handwritten document against us, which consisted of decrees and which was in opposition to us; and He has taken it out of the way by nailing it to the torture stake. Stripping the governments and the authorities bare, he exhibited them in open public as conquered, leading them in a triumphal procession by means of it. Therefore let no man judge YOU in eating and drinking or in respect of a festival or of an observance of the new moon or of a sabbath"
So here Christians were told not to let others condemn them, to make them feel that they were sinning, on the basis of their not keeping certain days, and mentions the Sabbath.
Also Galatians 4:8-11 - " Nevertheless, when YOU did not know God, then it was that YOU slaved for those who by nature are not gods. But now that YOU have come to know God, or rather now that YOU have come to be known by God, how is it that YOU are turning back again to the weak and beggarly elementary things and want to slave for them over again? YOU are scrupulously observing days and months and seasons and years. I fear for YOU, that somehow I have toiled to no purpose respecting YOU."
So here again we see that observing the Sabbath is not a requirement of righteousness for Christians today, that observing certain days was elementary and being a slave to these things.... and that we should now worship God according to the pattern set out by Jesus and the first century Christians.
In fact, the false religious leaders of Jesus’ day observed a weekly holy day, their worship was not acceptable to God because their hearts were wicked and and they were deeply involved in the political struggles of their day. They claimed to represent God. Yet they turned the Sabbath, which God had intended to be a source of refreshment for the Israelite people, into an oppressive system of man-made rules.