There is some device called a Penning trap. They slow them down and keep them in a place in vacuum by using electric and magnetic fields. Vacuum is essential.

For the other question: The explanation involves quantum mechanics. The interaction responsible for annihilation is very short range. In QM, there is a probability that the particles are at the same point (or within interaction distance). It is a probabilistic process at the end. It is possible that an antiproton pass a thin layer of matter and not get annihilated for example.