J.R. S. answered 09/06/17
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Unfortunately, the Lewis structure cannot be drawn here, at least, not by me. Your description of how you drew it is correct EXCEPT you didn't mention if you included a lone pair on the central atom A. I assume you did, if you competed the octet.
(b). Yes, the Lewis structure DOES show resonance. You can have B=A-B or B-A=B.
(c) The actual structure is an average/combination of the two resonance structures, thus the bond lengths will not be "pure" single or double, but a combination/average. So, one might expect the bond lengths to be approximately 135 picometers.