->Can you show up to Yosemite Valley in November without reservations and find accommodations?
Maybe for a night. Probably not. And very unlikely that you'd find someplace with availability for 4 nights.
->Is driving inside the Park challenging?
No. The speed limit on most roads is 35 mph. At some point in November or maybe late October, Tioga Road will probably close for the season. Glacier Point Road will probably close for the season. But if November is mild & warm, those roads may stay open. nps.gov/yose/planyourvisit/seasonal.htm
->Is driving into the Park from a gateway town (Groveland, Mariposa, Oakhurst) a hassle each day?
Yup. It's between 1.25 and 1.5 hrs to drive into Yosemite Valley. One Way. So every day you might spend 2.5 - 3 hours in your car, trying to get to someplace terrific. And you'd either miss out on the evening programs or you'd be driving in the dark. Some folks do it. I wouldn't. Your travel style will determine your best option.
->How can I find out what other lodging options are available in addition to the official ones?
The Top Questions on the right side of this page has a long article about Where To Stay.
->What is the weather likely to be during my November visit?
"Quite variable, with weather ranging from hot to cold, dry to rainy or snowy." Visiting in Fall: nps.gov/yose/planyourvisit/fall.htm