From the time the ATP-CTP course starts until the end of IOE, are there any breaks in between in which you can go home for a couple of days?

I had over a month after CTP before indoc. It’s not attached to a class date. You will also typically have a long weekend here and there among indoc, ground, and sims where you can go home. Depending on scheduling you will also have a week or two before IOE starts.

So basically, the answer is yes.

Which airframe?

CRJ: No breaks.
ERJ: breaks.