More on matter and anti-matter 
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*Does every particle that has rest mass also have an anti-particle with which it would annihilate?

*Does annihilation only occur between like particles?  For example what happens if a antineutron (anti u, anti d, anti d) collides with a proton (uud)?  What happens if a positron collides with a proton?

*Since the Tevatron accelerates antiprotons is this more difficult to handle and dump?

*I've read about WIMP annihilation detection.  Why would one assume there is any different proportion of WIMPS to anti-WIMPS than as is for non-WIMP matter (where there is far more matter than anti-matter).
 A: 
1.) Does every particle that has rest mass also have an anti-particle with which it would annihilate?

For fermions  in the standard model scheme , yes. 

The three columns on the left are fermions. Bosons are their own antiparticle and the term "annihilation" has no meaning other than "interaction" and whether it is probable. 

2.) Does annihilation only occur between like particles? For example what happens if a antineutron (anti u, anti d, anti d) collides with a proton (uud)? What happens if a positron collides with a proton? 

You have to figure it out from the SM scheme, linked above and the energies involved. An antiquark striking a quark will annihilate, the rest will interact.

3.) Since the Tevatron accelerates antiprotons is this more difficult to handle and dump?

It is more difficult to create and handle an anti proton beam upt to the energy needed for the experiment, as well as to build up a sufficient number of antiprotons in the beam. When entering the ring the handling difficulty is the same. Dumping is the same for both beams.

4.) I've read about WIMP annihilation detection. Why would one assume there is any different proportion of WIMPS to anti-WIMPS than as is for non-WIMP matter (where there is far more matter than anti-matter).

It depends on the particular model, and how one assumes the WIMPs appear during the cooling after the big bang. It is reasonable to assume that the same CP violation that created the observed asymmetry between matter and antimatter holds for WIMPS too. 
A: *

*Yes, for charged particles and some neutral particles. But there are so-called Majorana neutral particles that have no antiparticles (neutral pion or eta-meson, for example). In other words, a Majorana particle is its own antiparticle.

*At low energies a proton annihilates with an antineutron like a proton with an antiproton - mainly into neutral and charged pions (charge should be conserved). 
A positron does not annihilate with a proton. They have the same charge.
