When paper is recycled the ink has to be removed from the paper. They do this by pulping it together and then putting it through a number of washes with all sorts of different chemicals in it called surfactants.
A single piece of paper can be recycled up to 7 times depending on the fibres because eventually it becomes too short to be recycled again.
Before food is recycled it's sorted because clean paper is required. So different types of paper are used for different paper products. For example, paper that has been contaminated with food probably contains bacteria which would increase the risk of spreading this bacteria around the process.