I don't know how prevalent closings will be in Toledo on May 1, which is a Tuesday. I can only suggest that you go to the official websites of the key places you want to see and check for their hours. Look for the British flag on "EN" to switch to the English version of each website. A few of the key sights are: Cathedral, Santa Cruz Museum, El Greco Museum, El Transito Synagogue. Either refer to your guide book or look at a the Trip Advisor Things To Do List. Sometimes the TA page for a sight has a link to its website, which might be easier than Googling to find them for the purpose of checking their hours.
I love Toledo; it is a very atmospheric place and I consider it worth visiting even if you cannot go inside a bunch of sights you would otherwise like to see. For example, if you follow the link I've given you to Trip Advisor, you'll see three city gates shown on the first page. You can see all of those no matter what else in the city may be closed.
You can wait until you get to Spain to buy your RR ticket to Toledo (price doesn't change), but the RT ticket may be about the same price as a one-way ticket, and the return trains to Madrid sometimes sell out, so it's best to buy a RT ticket before you start out. Atocha Station in Madrid is large and rather confusing. Allow yourself plenty of time to get your ticket and find your platform.
For Spanish fast trains you will save money by buying early, but the best deals are on non-changeable/non-refundable tickets, so you must weigh the loss of flexibility against the savings. You can check to see how much early purchase will save you by looking at fares for tomorrow vs. fares for late May (or your travel date if it is sooner). Use the Renfe website or trainline.eu for this purpse. Renfe is sort of picky about payment method and doesn't much care for US credit cards. PayPal usually works.
Fast trains to Figueres stop at Figueres Vilafant Station. Barcelona-Figueres Vilafant ticket prices on the fast trains (and you don't want to use anything else on a trip that long) seem to range from about 11 euros to 29 euros roundtrip. If you buy at the last minute, there may be no 11-euro tickets left, and possibly only 29-euro tickets.
I haven't been to the Dali Theatre and Museum, but based on what friends told me after their visit last August, I'm confident that 5 hours at the museum would be more than enough time. [See Chani's comment below: It seems as if you may need 5 hours after all.] If you mean five hours for the whole trip, I am a bit doubtful. The train takes 55 minutes each way. Vilafant Station is about a mile from the museum (check this on Google Maps to be sure my memory is decent). There's a bus, but you might have to wait for it. You definitely should buy your museum ticket ahead of time, and of course you'll need to plan your transportation to allow for delays to assure that you arrive at the museum on time and won't miss your return train, so there's going to be some padding in there. Bottom line: I wouldn't count on being back in Barcelona within 5 hours of my departure.
Someone asked about the Alcazar in Seville recently, and it was suggested that the ticket be purchased in advance. I have never been to the Alcazar myself. For a lot of sites the wait isn't terribly long, so it's a matter of how you view the trade-off between flexibility of itinerary and standing in line. (If you were asking about Barcelona, there would be quite a list of places for which I'd say that you really, really ought to buy in advance.)
