Yes, there are hike-in spots at Watchman. I didn't stay at one but what i read was that they're only barely hike in -- park your car and walk a very short distance to the sites.
A lot. From 1 hour to couple of days. Angels Landing is recommended - it is relatively easy and with a gorgeous views
some camps are seasonal so I would call 1st
I don't think there is.
I meant more along the lines of camping spots that can only be reached by hiking in and roughing it. Places along the trails that are designated for camping in.
There is a shuttle every 15 minutes that will take you from the campsite to hiking areas
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