1) I don't know what "current" views on carbon is... but it absorbs impurities like chloramines until it's exhausted. I don't think it will leech it out once exhausted and you will probably have beneficial bacteria colonizing on it until replacement. To polish water, there is usually fine filter media for that.
2) Yeah, they are capable of doing cute things
Superman pose, stacking, claw your eyes out stuff.
3) Inconsistent (bad) diet/lack of calcium/lack of UVB lead to most issues with curling and bumpiness.
4) The nice thing about filters is that the good ones don't cost much more than the cheap ones, unlike filters. It's worth the extra cost.
Ballpark lifespan is tricky because they hide illnesses and injuries so well. Genetics also plays a bigger role than we realize. I think I've read about 50-60 year old terrapins but I would expect 25-30 years to be very good. My RES are 13 and still very active.