First off, about saving and reloading... that's not the way to play the game! The true way to play the game is to have your soldiers dying left and right until you can research appropriate technologies. Not allowing any of your guys to die so that they'll advance to become supersoldiers is just unrealistic. You should be playing to get as many of your soldiers killed as possible, while still winning the mission (or even failing a mission once in awhile). I'm not one of those hard-core freaks who say you can never roll back a bad result (these games are supposed to be fun, after all), but you're cheating yourself of some of the visceral enjoyment if you allow your guys to be perfectly safe by knowing you'll always resurrect them if they get hurt. This approach also has the Darwinian benefit of weeding out the troopers who suck. If they didn't survive the mission, they weren't good enough to stem the alien invasion anyway. Do you want to have subpar agents with humanity on the line?!?!? Besides, it's usually cheaper to hire (and pay) new agents than to equip them with the best stuff, bwahahaha.
OK, that said, the reason why X-COM can be so easy at times is because there's a bug in the save game code. Apparently, the difficulty level isn't saved properly, so you can be playing on superhuman, but as soon as you save and reload, bam, it's back down to supereasy. There are fan utilities to fix this, but it was unbelievably never addressed in an official patch. So if you want to play on superhuman for real, look up one of these X-COM utilities and try it out. Or you can play TFTD, which can be freakishly hard/tedious sometimes.
Next, finding the base in Brazil... Brazil can go to hell! Arrrr! (Just kidding, Edfilho.) Anyway, there are four major approaches to this. First, research, research, research. Your basic interceptors aren't going to be able to go head-to-head with a battleship, ever, as they're too weak to take more than 1-2 hits, and generally don't have the range to deliver a lot of hits before they bite it. Second, use multiple interceptors against a single target. A whole swarm might have a chance of downing a battleship, especially with improved weapons, although you'll lose a few. Third, send a troop transport on the scouting mission instead of an interceptor. They can loiter longer, so they have a better chance of finding bases and stuff. Plus you can send them in right off the bat when you find the bad guys. Fourth, just ignore the base and write off Brazil, focusing on the ultimate end game elsewhere. Concentrate on containing them while you exercise option #1. If you're too weak to intercept their probes, rely on your transports to tail the bad guys and send the troops in take down the big ships after they land. This also has the benefit of resulting in more loot, since the UFOs land intact.
BTW, where the corpses and stuff go is alluded to in some of the fiction Microprose released as a sort of teaser for TFTD. Basically, most of it is shipped off to government labs and stuff for military research, especially after X-COM is dismantled following the first invasion. Sorta an allusion to the whole Area 51 conspiracy nut type thing. This material was incorporated into some of the background material for the follow-ups, including Apocalypse and Interceptor.
Speaking of sequels, I'm kinda peeved that none of the prospective 3 "X-COM 4s" that were in the works actually made it out to completion (although I hear the PBEM X-COM Lite is a blast, provided you can find anyone to play with). I guess the projects suffered from a lack of focus, as making a solid follow-up to X-COM is what people really wanted, not 3 different types of games all set in the X-COM universe. Although that 3D squad shooter thing looked like a real winner, they probably could have released a half-assed effort and still raked in some bucks.