Bi-Wire

Bi-wiring speakers doubles the cable going to the speaker - if the speakers are biwireable then each set of drivers gets a cable thus being driven individually from the amp with the same power going to each speaker - channel a and b do not go to the same speaker - L (a) channel goes to the left and R(b) channel goes to the right speaker. Some amps make it hard to run that amount of cable from its speaker out posts. If it is easy then there may be improved sound that comes from the speaker - this is always a source of great debate. Some confuse biwire with biamping which is a totally different story.

No - if your receiver has two sets of posts for two sets of speakers like speaker A and Speaker B with two controls in the front labeled as such then you would hook them up :(A - left) to Speaker left one set of post--then (A - right) to speaker right same post on that speaker as (A - left). Then (B - left) to Speaker left on the post not used - Then (B - right) to Speaker right on the not used post. To run the system you must have the Speaker A and B buttons pressed in on the front of the receiver. Make sure the jumpers from the speakers are removed.

Yes -- If you are saying A and B for your two separate channels for one set of speaker outs meaning left speaker and right speaker then A - Left receiver to Left speaker and then B -- Right receiver to Right speaker only you have to do two runs to each speaker from the same channel.
Make sure the jumpers from each speaker are removed.