For every particle there is an anti-particle - implies there are equal numbers of each. This is not the case. You probably knew that but wanted to clarify it, anyway.
For every particle, there can be a particle of Opposite Charge, which would be an anti- particle. Should they come into contact, they would annihilate which would nearly totally (But not totally) destroy both.
If a particle takes up space, an anti-particle takes up the same amount of space. A particles anti-particle behaves and has properties that are essentially identical to its counterpart. The only real difference is the Charge.
A Positron (anti-electron) for example, would pair with an anti-proton to make anti-hydrogen. The anti-hydrogen would be identical to normal hydrogen in every way. Would behave the same way...