There have been complaints on this forum about difficulty in using a Spanish rail pass, but I don't know whether there's only one of those. The situation did not sound good, however, so at the very least, I'd recommend doing some Googling to see if people are still having major issues, and which pass--if there's more than one--is involved.
Even traveling as soon as March, you can probably save a good bit of money by purchasing rail tickets now rather than waiting until you're in Spain. You need to check the fare rules carefully as to ability to get a refund or reschedule if your plans change.
Trains between Madrid and Toledo are the exception in that the fares on that route do not increase as the travel date approaches. The only potential issue there is that those trains do sometimes sell out. (Rick warns about this in his book, recommending that you buy the return ticket at the same time as the outbound ticket.)
Actually, I have observed a lot of cases of "train full" when I looked at current-day and near-future schedules on the Renfe website for trains on the main lines running between Madrid and Barcelona, Seville and Granada. There is some risk of not being able to get on a train at the time you want if you wait too long to get your ticket. How big an issue that is in March, I do not know.
Whatever you do, don't plan to buy tickets at a staffed counter at Atocha Station in Madrid. You will waste hours doing that. The vending machines are easy enough to use for standard tickets, but in the past there were occasional complaints about US credit cards not working. I haven't heard that recently, but I think more and more people are buying their long-distance tickets before leaving home, because the savings can be substantial.
Folks like the Renfe app, which I haven't used. As noted above, there are now competitors to Renfe running trains on some of the major routes, so to see all your options you'll need to use a third-party website like trainline. Most if not all those will charge a fee. You could use trainline just for research, and then buy the tickets from the appropriate operating company's/companies' website(s).
The fast trains require seat reservations, and they are included in the fare if you buy tickets. It's only when you're using a rail pass that you are charged extra for the seat reservation--one of the reasons many of us are so doubtful about the value and practicality of a rail pass. As far as I know, seat reservations aren't available on the non-express trains, but your itinerary doesn't appear to include any of those.