I have these two tables that are very hard to replace, so I want to fix them instead. The problem is that they have scratches, bumps and I don't even know what else. What is the best way to fix them, preferably with products that can be purchased from Amazon or something.
That looks to be particle/press board (basically glued together sawdust which is pressed into a flat board) covered with a laminate (might be melamine), which is not very friendly when it comes to repairing. The wood itself tends to crumble when messed with. The "bumps" are where moisture has gotten to the particle board under the laminate surface.
The best you will be able to do would be to either live with the bumps or try to carefully plane them down using a "cheese grater" plane, then sand out all nicks scratches and bare spots to blend. Fine sand the entire top and clean thoroughly with mineral spirits. Use a "difficult surface" primer like BIN, then coat with a quality high gloss paint. use a professional grade brush or it will look like crap. All products mentioned are available from Amazon.