[Campion]

After Constantine was the power of the State ever used to punish heretics?

That idea was mainly an invention of the middle ages. Heretics in the era you're talking about were typically removed from church offices (good) and banished to remote locations (maybe not quite as good).

After Constantine did worship services change?

Not very much, although the use of Greek died out in the West and was replaced by Latin.

Did the places of worship change, after all prior to Constantine Roman Catholicism was largely a faith of the poor.

You mean you admit that "Roman Catholicism" existed prior to Constantine? I'm shocked.

After Constantine what happened to the pagans?

Well, one of them, his grandson I believe, became Emperor and tried to stamp out the Faith. qv "Julian the Apostate"

[Campion]

... prior to Constantine Roman Catholicism was largely a faith of the poor.

Oh, BTW, that's not absolutely clear. The word "pagan," for example, comes from a Latin term meaning "country person" or "bumpkin". And we know that Christianity was popular in the military and other fairly prosperous and powerful strata of Roman society.