I used to remove the capacitors by desoldering them, but I managed only to pull a pad every other time, which gave me headaches.
Now I use the method of twist and pull with pliers, with that method, I never pulled a pad. You grab the capacitor with pliers and then you twist it left and right few times. Do not pull upwards! Usually they are so corroded underneath that they will break loose after one or two twists.
You can also use SMD hot air station to remove them, but you will usually melt some plastic connector or something that is near the cap...
About cleaning the board, rubbing alcohol is good, but when the board has a lot of corrosion or residue left, it would often not help much. Use vinegar or a limescale remover instead.