In an audio magazine I read a long time ago (probably Audio, now sadly out of publication), someone mentioned a system that worked for dewarping:
Take two rectangular sheets of flat glass at least 12.5" on a side. Clean them fanatically. Clean your LP as well. Sandwich the LP between the two pieces of glass and “bake” them in the oven at the lowest setting. However, I forget how long they recommended baking them.
In theory, a rim weight should work, but I’ve read recommendations against using weights (they were talking about spindle weights, not rim weights, although I believe it would be the same issue) on turntables that were not designed for them - the additional weight could damage the bearing(s). Some audiophiles use weights or clamps to “couple” the record more tightly to the platter. I don’t recall what the advantage of this was. A weight heavy enough to remove a warp could also have a (temporary) adverse affect on the suspension, depending on the design of the TT.
Discwasher, is, apparently still in business, and now owned by Recoton. For about half my record-playing life I used a Discwasher record cleaning brush, for the other half I swore by the Watts manual parastat (apparently still available at audioclassics.com), which seemed to do a better job, but was more difficult to maintain.
Discwasher also offers (offered? their website is down right now) a stylus cleaning brush for a few bucks. Definitely better than flicking the dust off with your finger (although I have to admit I’ve done that several times). A worn or dirty needle will greatly reduce the life of your records, as will using too heavy a tracking force. Most good cartridges are designed to track at between 1.25 and 2 grams, anything outside of that range will likely cause more wear. You should learn to balance your tonearm (it’s very easy, and doesn’t need to be redone unless your turntable is moved, since the weight can shift). Cheap turntables used springs rather than weights; these should be avoided as they were generally sold with inferior “ceramic” (ceramic referring to the way the signal was generated, by flexing a piece of ceramic or crystal, not the material they were made from) cartridges, which use much heavier tracking forces than the superior “magnetic” type (which create a signal by moving a pair of magnets within a pair of coils), or sometimes the other way around (if you were willing to spend a few hundred on a “moving coil” cartridge).
BTW, eBay is a great place to pick up good-quality vinyl related stuff for a song (NPI).