Let me start off by saying that I am 100% Jewish and believe 100% that Jesus is the Messiah. Not all Jewish people reject Him as the Messiah. Remember, the early believers were mostly Jewish for the first 50 to 100 years.
And even the Jewish prophet Isaiah said most would not listen. “Who has believed our message?” (Isaiah chapter 53 verse 1). In other words, Isaiah is saying, most Jewish people will not believe when they hear the message.
Of course MJ’s are not looked at as Jewish by the rest of the Jewish community, but thankfully they do not determine truth - God does - and Messianic Jews seek to please God rather than other Jewish people - most of whom know only Jewish traditions. (There is a difference).
Now - in answer to your questions..
1) In a Messianic congregation there will be a mixture of Jewish believer in Jesus (like myself) and Gentiles who are believers in Jesus and love the Jewish culture and flavor of worship.
2) ** Messianic Jews observe traditional Jewish holidays such as Purim and Chanukah, the ninth of Av and the Ten Days of Awe.
** Messianic Jews observe the biblical feasts such as the Feasts of Trumpets, Tabernacles and Passover.
** Messianic Jews worship on the biblical sabbath, i.e., Friday evening till Saturday.
** Messianic Jews cant the Sh'ma, the kiddush and motzi, the Aaronic benediction, Etz Chaim, and many other parts of traditional Jewish liturgy.
** Messianic Jews read the Torah portion in Hebrew at worship services.
** Messianic Jews bar mitzvah their sons and bat mitzvah their daughters.
** Messianic preaching is mainly from the Hebrew Bible (Tanakh), although references to the B'rit Chadasha (New Covenant) are not unusual.
** Messianic Jews emphasizes the special relationship between G-d and the Jewish people.
** Messianic Jews emphasizes Jewish traditions that do not conflict with the Bible.
** Messianic Jews understand that G-d never changed the way to obtain salvation: "And Abraham believed G-d and it was credited to him [Abraham] as righteousness." The purpose of following the Torah (often mistranslated "Law", but literally, "teaching") always has been to live holy, not to obtain salvation.
** Messianic Jews teaches the biblical doctrine that salvation is a free gift from G-d, by faith in the atoning work of His Messiah.
3) Have you read any messianic Jewish authors? You can Google some and you will find some good information.
Hope this helps!
I am an Author and a Jewish Believer in Jesus (a Messianic Jew) for 26+ years.