Hey Matt,
I'm sure you'll get more verbose answers from our more seasoned vets of EP but we travelled in September so I can definitely help you with that...
1) We did the Tue 19th and the Wed 20th on the park in September and got on everything we wanted on the first day, including 3 times on Woden and Blue fire. The only things we missed were universe of energy, a couple of flats, shows and the 3D Dome. The longest queue was about 30 minutes that day. On the 20th the morning was considerably busier and it throughout the day there just seemed more throughout the park. All became clear once we realised that Traumatica (EP Halloween event) was starting that night. This meant that Greece shut early and the queues were noticeably longer with BF quickly going up to an hour. (more like 40 to be honest.)
TLR try and avoid the Halloween event, however 3.5 days should be more than enough even if you do clash with that date.
2) We were determined to stay on site so decided to stay at the Alcazar. As far as I remember all the resort hotel prices are comparable to each other, with different tiers of room prices. I'd pick the hotel that appeals to you the most. (I'm sure stopping in rust is cheaper but you wouldn't regret expanding your budget to stop on resort if needed.)
3) Definitely go by hire care if you want to do other things in the area and you want convenience.
4) I'd recommend Triberg Waterfall and the house of 1000 clocks (the one slightly outside of the Triberg town centre). There is lake Titisee which you can take a boat ride out onto and then you could head to Todtnau for the Hasenhorn alpine coaster or trek up the mountain.
If you drive out the Basel, I'd recommend going via Colmar. You will know you are near when you see a roundabout with the Statue of liberty on it (the designer was from Colmar and this was a tribute to him.) It also features a Little Venice area of which you can get some nice food and drink in the area. Also if you are a fan of studio Ghibli, visually Howl's Moving Castle was based on parts of Colmar and Mason Pfister is building that you can see in the anime.