Welcome to TE and congratulations on riding again! It sounds like you are headed in the right direction. I would say that most of us here started with a hybrid and moved to a road bike.
To answer your questions:
1) No, you are not out of your mind for wanting to do a century. You will have plenty of miles on your legs by next spring.
2) I've seen people do centuries on mountain bikes--I wouldn't but I've seen it. I think you can get a really nice new road bike for around $1000 that would do anything you would need it to.
3) Of course, it's ok to continue to "train." Just ride your bike and have fun.
4) If you are talking clipless pedals, that's a very personal decision. I would recommend you getting them and be comfortable using them before you do your century. You could put them on your hybrid now and learn how to ride in them and switch them to your road bike when you get one.
5) Saddles are a very personal choice and there are a lot of threads here on TE about them---just do a search. The pain in the tailbone issue is one that should be addressed by someone else. I've not had any experience with that. I will say that may have to do with proper fit and would recommend that you go to a reputable bike shop to buy your road bike and get a proper fitting.
Keep riding and have fun.
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"We don't stop playing because we grow old; we grow old because we stop playing." George Bernard Shaw
Luna Eclipse/Selle Italia Lady
Surly Pacer/Terry Butterfly
Quintana Roo Cd01/Koobi Stratus
1981 Schwinn Le Tour Tourist
Jamis Coda Femme