as a non jewish believer i think (and this is just my take), that when people come to faith, they are grafted into a tree (an olive tree). The roots of this olive tree are the patriarchs (abraham, isaac and jacob). The jewish people (israel) should be natural branches, in the sense they ought to show faith, but some do not and so they are broken off. The non jews, who do not normally show faith toward the God of Israel are referred to as not being natural branches belonging to this tree. The tree is the tree of faith. (romans 11). Super passage either way!
Paul speaks that when a non jewish believer turns to faith in the God of Israel, they are brought into the commonwealth of Israel, and as such are privledges of the blessings that brings. These blessings include the Torah (wrongly called the 'law', with all its fullness).
God said to Abraham, i will bless those who bless you... and the same holds true for his descendants... God will bless those who bless Israel.
But to the question... In the book of Acts we see a man called cornelius (whose family were the first no-jewish family to recieve the baptism of the Spirit). This same man is mentioned earlier in the gospels. He is referred to as a God-fearer. That is someone non-jewish who wants to serve the God of Israel. He followed their way of life, the calendar, their feasts and their diet, and probably as many aspects of Torah as he was able (as he had not converted to the jewish faith - he had not been circumcised).
Jesus said whoever teaches others to obey the least of the commands shall be called the greatest in the kingdom....
Now as a non-jewish believer, you have the right to participate in the lifestyle. In changing you're diet it is pleasing to God... this diet things is not a law of moses thing. It existed long before the law came into being. (some christians think the dietary laws (even for jews) are no longer binding on them but this comes from misusing the scripture and not reading in context)). The keeping of the seventh day sabbath also existed before the law, right at the beginning of creation (how many christians actually really do set aside one day to REALLY rest). At the creation of the universe, the festivals outlined in Leviticus 23 were already planned by God, and so the moon is referred to as a 'mo'ed' (a sign) a very unusual word.... but the feasts are referred to as the 'mo'edim' signs showing the creation of the moon is linked to the feasts.
Some people think that the feasts are a shadow and therefore irrelevant to us... however looking at colossians which everyone uses to support this position, we see the signs are a shadow of future things, not present tense things, so we see in celebrating the festivals Jesus being outworked. So theoology is not just learned, it is eaten... taste and see that the Lord is good.
Lastly and I know it has been a wordy reply... when the church was established, Jews said, to gentiles have to be circumcised and convert to judaism before they can count as real believers? Now the shoe feels like it is on the other foot and we effectively say, does a jew have to convert to a supposed religion called 'christianity' to be acceptable? In both instances the answer is an emphatic No!... Jews do not need to convert they just need to show living faith in the redeemer.
All this aside, many of the issues you have raised are good things, prayer, practicing Jews have a super prayer life, and their entire life revolves around their maker from morning till night. Some christians ask 'aren't they just legalistic in following the law' - i answer if their actions are borne out of love for God and a desire to please Him by doing what he asks then that is good.
Keep the questions coming!