The in/out rule is badly named, but to answer your question as long as you board all the trains between 0000 and 2359 CET (If in UK it is 2300 to 2259) they only count as one travel day, even if you leave your last train after midnight. (It is actually based on scheduled departure time not time of leaving if delayed).

The actual way the rule operates is that for up to 2 travel days of your choice you can use the pass in your Country of Residence as if you were in any other country. This means you can use these 2 days entirely in your COR, to cross borders in any direction or even not at all. You can also travel on as many trains as necessary on each travel day.

Yes, it will. You can use as many trains as you want on any travel day, also in in your country of residence.