You can accomplish a great deal at Plitvice by arriving in the park mid- to late-afternoon, seeing some of the park then, and finishing up the next morning, going inside when the park opens. Although there are additional paths not included on the labeled routes, I think one night is the sweet spot for most visitors and wouldn't recommend 2 nights when you have only 10 or 11 days in total. Just don't try to drive in from Zagreb or Split and plan to see the park beginning at 10 or 11 AM. That will mean being surrounded by an unbelievable number of day-trippers.
The park has a new ticketing system that involves reserving a time-slot ahead of time.
I mentally write off my arrival day because sleep-deprivation and jetlag mean I rarely accomplish anything at all, so I wouldn't count that day as available for sightseeing in whatever turns out to be your first city.
Time in Zagreb should depend partly on your interest in art and decorative art museums. It has a lot of them. I especially recommend the small but wonderful Museum of Naive Art. In the not-art category, the Museum of Broken Relationships is popular and fun. Not interested in art? In that case one non-jetlagged day in Zagreb would be OK. Love art? You'd be hapy to have two non-jetlagged days and would need to plan carefully to fit everything in. The historic district is worth several hours of wandering.
If you like art, check the websites of the Zagreb Museums for days closed. If you don't have a guidebook that covers Zagreb well, consult Trip Advisor's Things To Do list to see what museums sound appealing.
There's a possibility the weather may break before the end of the yrip. If that happens, the south may remain pleasant a bit later than Zagreb. All other things being equal, I'd prefer to start in Zagreb. However, after consulting airfares and schedules you may find that things are not equal. And there's a good argument for going straight to Dubrovnik and getting over your jetlag there.
It's mostly buses in Croatia. I've been to all your destinations and have never rented a car in Europe.