With regards to Psionic damage and mechanical units, you need to look at it from 2 perspectives:
Lorewise: Psionic powers do not interact very well with inert (i.e. non-living) materials. This is a double edge sword, on the one hand trying to protect yourself with these materials is pointless, since the psionic power tends to go straight through it. On the other hand, however, for something which is mainly made of these materials, actually affecting that thing just doesn't work very well. This is represented in game by mechanical units having a large (4 atm) resistance to psionic damage and effects. Most mechanical units do have living crew, so the status effects will work, however they are still resisted due to the difficulty of actually making contact with those minds (the psionic attacker can't easily "see" thje mind inside the machine). Robot units have the "mindless" attribute, which makes them completely immune to those status effects (though you can still damage them with psionic power).
Mechanically: Psionics powers are really strong: Bypassing armor gives a huge bonus against half the units in the game, while psionic debuffs (mind control, panic, etc) can have battle winning consequences. We need a counterbalance to stop them simply outclassing everything else, and limitations against mechanical units (about 1/3 of the game's units) is a good way of doing that. Right now, this is just done with the resistance, in the future we might make them immune to psionic status effects too. It all depends on how balancing goes during the beta.
As for biochemical attacks, they are effective against mechanical units, there are no special resistances or anything. However, most biochemical status effects are things like Poison and Disease, which do not work against mechanical units. This makes biochem very good at damaging machines (especially with the arc damage mod), but not very good at manipulating them.
The end result of this is that Kir'ko are just not very good against mechanical units, they do have options, but a smart player may want to pick a secret tech that gives them an extra boost in that area.
No, Commander's are the Kir'ko elite, and the males have been genetically modified to allow use of psionics!