Well, the biggest difficulty in answering your questions, is the same difficulty presented by many other martial arts- imitators. What applies for genuine Sistema might not be reflected in imitations.
It's, generally, a hard style, emphasizing striking and grappling, along with weapons skills (including firearms).
From what I have seen, the emphasis on countering weapon attacks is to "make the weapon moot", so to speak (moving it off-line, trapping, etc.) while simultaneously counterattacking the attacker.
Most of Sistema's curriculum is preemption-based.
The use of "psychic" should probably be preceeded by "for want of a better translation" (from Russian)- they are referring to "gut feeling", "well-developed intuition", "clarity of thought", and other concepts which are pretty commonplace in other nations' martial systems.
A good source of information on Sistema is James Williams. His site is http://www.dojoofthefourwinds.com
Hope this helps.