1- Granted.
2- Not quite. One who does melacha on shabbos publicly is a shabbos desecrator.
3- Repeat, not quite. See ???? ????? compiled mostly from psakim of Rabbi Shlomo Zalman Auerbach. The custom is to count anyone without asking questions about ideological purity. (Otherwise you couldn’t find a minyan anywhere because in our time you can’t get 10 frum Jews to admit that the other nine aren’t heretics.)
4&5 – Not at all. People excluded from the community lack ??????, that is no one else can trust them that the food is kosher. Stam yenam and bishul yisrael are a penalty imposed on the sinner to exclude them from the community. None of these penalties were ever meant to apply to the individual himself, who knows the food is kosher. An example of this can be found in ?????? ?????? 8:8.