Car rental in Croatia

I think you will always get a better rate by booking in advance. Again you will get better rates by going through a consolidator, than by going direct to a particular company. I have used http://www.arguscarhire.com/ and their sister site http://www.holidayautos.co.uk/ over the years. On both sites you can specify an automatic, plus where you want to collect and drop off the car. You can check the terms and conditions for different rental companies there too. You need to look at the charges for 'Cross border travel' since going up the coast from Dubrovnik, at the town of Neum, you cross into Bosnia and Herzegovina for about ten kms.

For what it's worth, there is great bus service from Dubrovnik and Split and vice-versa - inexpensive and modern buses traverse the coast and make the journey hassle-free (you stow luggage in a large compartment underneath like any other long-distance bus). It's likely similarly easy to get from Split to Zagreb (I haven't been that far north, but I assume even a train is an option?). The only trip where a rental car would come in handy is if you made the trip to Mostar only as a day trip (no overnight). When I went to Bosnia & Croatia, I began my journey in Sarajevo, then went to Mostar (with an overnight there; in retrospect I could have used one more day) and then to Dubrovnik by train and bus. It was easy and inexpensive although the train was a bit slow and old. I have a feeling an automatic rental will cost quite a bit so keep in mind the other option (or just rent a car for Mostar if you want to get back the same day).

I did the Dubrovnik-to-Zagreb run by bus last year, though I broke the trip in Zadar rather than in Split. It was comfortable. If you want to take a look at the bus options, this website may be helpful: Bus Croatia. As always in the Balkans, it's best to reconfirm bus schedules on the ground, and if you know for sure when you want to travel (I usually don't), it might be a good idea to get the tickets ahead of time.

A couple of years ago, we rented a car in Croatia from a local company, but arranged through AutoEurope. We picked up in Dubrovnik and dropped in Zagreb. No charge for doing that. Since the per day cost drops the longer you keep the car, I think you'll be better off just keeping the car. Getting automatic anywhere in Europe is dicey. I would definitely reserve ahead.
We crossed the border of Bosnia and back into Croatia with no problem. I'm remembering that we just whizzed out of Croatia, but there was a passport check when we re-entered. My sense was that it had to do with coming into the EU. Nothing to worry about.

I think renting cars for one day on 3 seperate occasions is a mistake. First of all one day rentals will be more expensive and more hassle (especially if you have to get an automatic) and one way rentals are usually more expensive as well.
Secondly there are good bus services between the cities you want to visit, so renting a car to get from A to B seems a bit odd.

My advice would be to either rent a car for the whole duration of the trip or to rent a car for a day or two for day trips (like the one to Mostar, but that can also be done as a tour with an agency) and do you transport from A to B by public transport.