Can I construct sentences like a) and b) below, instead of c)? I understand the construction in c) is the most common and acceptable one. a) Try to deliver the gifts without you are seen. b) Try to deliver the gifts without your being seen. c) Try to deliver the gifts without being seen.
a) is not grammatical in most varieties of English : without introduces a noun phrase or an ing clause, not a finite clause. (There are some dialects which allow it, I think, but no standard varieties).
b) is grammatical, but unusual: we usually don't express the subject of a subordinate clause when it's the same as the (actual or implied) subject of the matrix sentence.
Note also that, while the possessive your being is what the traditional grammar books say, many people now don't use it, and would say We'll go in the back way so we can get in without you being seen. (I've used a different sentence in which the you(r) is more natural). Your being is certainly not wrong, but some people would regard it as very formal.