I think the number of daily buses to Plitvice varies with the calendar, but you certainly can get there easily from the Zagreb bus station (which I will warn you is a bit longer walk from the RR station than it appears on maps). Then there are buses on to Split as well, though I've always made a round-trip from Zagreb.
The BusCroatia website is good for preliminary planning, but throughout the Balkans I think it's best to double-check the schedules at the bus station when you reach each city. And I found buses back to Zagreb frequent, but apparently not running on the schedule I had been given. I wouldn't plan to take the last bus of the day, and I would plan to get to the bus station/stop early.
Although you might (I give no guarantee) be able to run into the Zagreb bus station, find the Plitvice bus and pay the driver, you will pay more than if you buy tickets at the ticket window upstairs. There can be a bit of a line, so don't push your luck there. For the onward trip to Split, I assume you'll just pay the driver. There are multiple bus companies going to Plitvice, so buying the onward ticket ahead of time might not be prudent.
Booking.com has some listings very near the park in Plitvice. Some may have shuttles, but I think some are within walking distance. There's at least one hotel (I assume more expensive) inside the park. I have not stayed in any of the local lodgings but agree that it's the only way to have a good experience in the park these days, since you must be there early and/or late to avoid day-tripping mobs.
In Zagreb I stayed at the Best Western Premier Astoria. I'd call it a business-class hotel. It's not too far from the train station (a bit farther from the bus station, but so is just about everything) and convenient to several large museums. You'd be able to walk to the very nice Old Town, but it's far enough that you might want to take a tram.
Edited to add: I would not take any one-day bus tour from Zagreb to Plitvice unless the bus departed at something like 6 AM. Otherwise, you'd be arriving at the same time as the day-trippers on the public buses. I made that mistake in 2015, and the experience was memorable, but definitely not in a good way. The park is wonderful (I know, but I had visited it twice before), but not if you're only there between 10 AM and 3 PM. The walkways are massively overcrowded.