Yes, to all of the above. No need for a car seat for either one on the plane. Our 3 yr old has been on 30+ flights since she was a newborn, when she started having her own seat we bought the CARES harness and talked about the flight, what was going to happen, the "rules" about seat belts (and noted that the rules are made by others, not us, and if we don't follow the rules we won't get to ride the airplane in the future). Also the only time she is allowed to watch movies on the Ipad is on a flight. We got Tangled, UP., Frozen, TOy story, etc but all she wants to watch is Frozen, over and over and over again. Another thing that is good for the 2.5 year old is Melissa and Doug removable/reusable sticker books. Depending on your child's personality, you may want to tell them there are special treats/things they can do, or let them see the activities/movies, what have you and tell them that they are special for good behavior on the plane. Also, make sure the kids are not tired or hungry before they get on the plane!
I'm also more relaxed about having them strapped in for the whole flight. we make frequent trips to the potty, allow them to get unstrapped if the seat belt sign is off, etc. Also if there's particular snack treats they don't normally get at home, make little goody bags for them to have on the plane.
Oh - and for the 2.5 yo definitely remember to bring their security object or blanket. Even if it's not something they use all the time when at home, they may want to hold it while on the flight.