1 - Rocker makes it more difficult to properly carve a ski. Carving is not the only way to turn a ski but it is a core skill that all skiers should have. It seems to me rocker is mainly useful when you are going off-piste or skiing powder. These are not the conditions most average skiers actually ski.
To properly carve a ski has nothing to do with rocker - Carving is largely determined by the radius. The wider ski takes more angulation to set the carve, but rocker has nothing to do with it.
2 - Wide skis are more difficult to carve than skinnier skis. Not really more difficult, just takes more angulation to get set the edge. The edge-to-edge will be slower, naturally, and that's a trade-off. Does that mean more difficult? Perhaps
3 - Wide skis are more stable. This can be good or bad. The extra stability means you can go down faster with fewer turns. (For me, they "shrunk" the size of my local hill. But that is just my personal taste. ) Not to be a jerk, but wide = float. Stability comes from other things like running length, stiffness, dampness, and lateral beefiness. Maybe its a coincidence that wide skis are stable and can cruise, but probably because many of them are advanced skis, meaning they are designed to be stiff, damp, laterally stiff (and these days with rocker).
In my humble opinion:
Daily ski for East coast - probably should not exceed 85 and do not need rocker at all. I ski the east. My dailies are 86 and have tip and tail rocker. 40% of the time I ski a 97 with tip rocker. moguls, trees, groomers - what ever is good. (That being said, the year I am adding a pair of 78s w/ full rocker to the quiver because I love to carve.)
Daily ski for West coast - varies a lot depending on local hill, but if you are hitting a lot of groomers 80-95 width seems to be the sweet spot. If you are mostly off the groom, maybe 105-110.
For powder - go as fat and as rockered as you want When I ski out west lately, I don't see many advanced skiers with anything under 90. 80? Nope. Average - a guess - is well in the 90s.