Are there TER or Intercités trains which need reservation for travel inside Île-de-France, in second class? If yes, how does one confirm whether a particular train needs reservation before boarding?
Yes you can. All these three tickets can be used on all trains within the Ile-de-France region, including TER and Intercités.
There are some restrictions though:
You have to be sure that your ticket is indeed valid in the zones you want to travel, for the whole journey. If it isn't, with a Navigo pass, you can purchase a complément de parcours (you need to buy it just before your trip at your origin station). Note that a Navigo monthly or yearly pass (but not a weekly pass) is valid for the whole Île-de-France region on week-ends and public holidays. With Mobilis or Ticket Jeunes Week-end, your pass must be valid for the whole journey.