Like RDS1220 said, coffee filters are about the best household item you're going to find. I'm not too keen on the use of a Q-tip because the cotton likes to clump or leave pieces of lint behind. As long as it's soft and has a very tightly-knit construction, then you cannot go wrong. For the solution though, I'm a big fan of heptane, it evaporates within a second or two and leaves absolutely no residue.
IMO coffee filters are great for cleaning thermal paste from the CPU and heatsink. I use a dry coffee filters to get off as much of the junk as possible then wet filters to finish the cleaning.
Coffee filters dampened with 95% isopropyl alcohol works great. Lint free and dries quickly. Most clothes leave microscopic fibers behind that interfere with the heat transfer and leave dead air spaces between the CPU and HSF
No but it's not non lint so it could leave little fibers behind that could affect temperatures.
Air is full of dust that will land on your lint-free PSU, HSF and paste between the time you are done cleaning and the time you are done putting it together. If lint particles are too small to be visible to the naked eye under normal lighting conditions, it is unlikely to have any measurable impact on cooling performance.