Is train travel restricted on holidays like Easter?

I guess I can not say for certain, my hunch would be that they are as normal, perhaps the best would be to go to Dbahn site or SNCF and query that for the trip you are looking to make. If the schedule fits your needs, then it matters little whether it is restricted or not.

Generally yes but not always because Monday is also holiday. If it says train runs on the non work day before work day in this case it would not be Easter Sunday. You don't have to be worried about this if you are using online schedule. Just put your day of travel there and it will tell you your schedule on that particular day.

Sunday and holiday schedules are usually the same, but the exact schedule options for your travel date are online, as others stated.