Croatia itinerary

1) Sure. I'd look up a few places in Hercegovina to make use of the car.
2) I would try to at least pass through Split to see Diocletian's palace, but of course you cannot do everything and have to prioritize somewhere.
3) I've only done it on the bus, but it's a short ferry hop between Korcula (ferry port is a short drive from old town) and Orebic.
4) I mostly spent time around Kotor, other than a brief visit to Budva. But from reading, I think the interior would be more interesting, especially since you will have coastal time in the Korcula area. If you have time to tour the area independently I would do so, but not sure I'd bother with a long day trip from Dubrovnik.
5) One of the best places I ever stayed was a small apartment outside the city walls up hundreds of steps--totally worth for views of old town and the sea. I like a view--inside old town can be noisy.
+ Don't know Slovenia
One night in Plitvice is sufficient unless you are true nature nuts. Try to do a short evening walk, then get up early the next morning and do the lop before leaving.

I've been to Croatia and Slovenia a few times. Click on my name to find my websites and you can read a few of my trip reports and look at the pictures.

I think late September/early October is an excellent time to go.

Mostar is small - doesn't really need a lot of time to see the old town, but it gets busy with tour groups during the day. That's the best reason to spend a night: to see it when it quiet, not so busy. Well worth seeing, though.

I did not drive to Korcula - I took the bus from Dubrovnik, and our bus used that ferry at Orebic.

I spent only a night in Kotor for my visit to Montenegro. I didn't fall in love with the city of Kotor, but the scenery around the Bay of Kotor is breathtaking - I'm very glad I drove with the ability to stop along the way vs. being stuck in a bus. You could rent a car for just a day, if you won't have wheels at that point in your trip, instead of a guided tour. You might also higher a driver to the day or something.

I stopped at Perast along the bay - really lovely little town. Kotor was convenient and I don't regret staying there, but I kind of wish I had stayed in charming little Perast instead. Whether you want to spend more time in Montenegro depends on your priorities on this trip - you have only three weeks and that's really not a lot of time for all the places you want to cover.

On my first trip to Dubrovnik, I dropped off my car as I arrived so didn't have one - and stayed just outside the Pile Gate (very flat, no steps). I found this an excellent location - a very easy walk into town. You can stay in town too inside the walls but it can be louder and a lot more expensive. If you have a car staying there it may be expensive to park it. I haven't been to Cavtat, but I hear it is lovely and quiet compared to busy Dubrovnik.

One night should be plenty for Plitvice. If it matters, the park ticket prices drop by more than 50% on October 1 (I first visited in early October - some pretty fall colors). The best way if possible is to arrive the first afternoon, visit part of the park later in the day by the time tourists start to leave and see the rest in the morning - enter the park as early as possible the second morning to avoid the tour groups that clog up the trails by late morning. You can get a gist of the whole park in about 6-7 hours.

Krka is a really lovely park too. Different from Plitvice. The massive Skradinski Buk cascading waterfall dwarfs anything you will see at Plitvice. But I prefer Plitvice - dozens of little waterfalls, seemingly around every turn. If you like to swim, you can swim below Skradinski Buk (I didn't) but not at Plitvice. Up to you whether you need to see both. You could limit your Krka visit to just Skradinski Buk (park at Skradin and take the boat up to the falls and back), but there is more to the park than that. The highlights are more spread out than at Plitvice.

I drove the "Julian Alps Loop" in a single day - from Bled up the Vrsic Pass and down into the Soca Valley. If you want to stop for "back to nature" experiences or something, you might split it up over two days, but I found no need to. It's just a lovely drive where you can stop here and there and take your time and enjoy it. I think I drove it in half a day with a lot of stops.

Know that if you rent a car in Slovenia and return in Croatia, it might incur a very expensive one-way drop fee FYI. Many people avoid this by having a separate car in Slovenia or not one at all (but you'd need one for the Julian Alps Loop drive of course). You could drop the car in Ljubljana and take the train to Zagreb or Rijeka and pick up a Croatian car there and return it in Dubrovnik.

We are actually renting our car in Pula after a ferry from Venice. Seeing Istria for a couple of days, then driving to Bled for the beginning of our Slovenia part of the trip. But thanks anyway!