OK so here goes.
blue = the answers.
Ayer fue el cumpleaños de Olga y
ella ___pasó muy bien.
so the answer is lo. however the part that confuses me is - duh it just struck me - she had a good time, not Olga. so ella is the OI but since she experienced the 'joy' thus not necessary and therefore the implied DO is cumpleanos (havent figured out how to do the accents and ~) and so thus LO.
The answer is correct in Spain, but not in other coutries, and your approach is wrong. "Ella" is the subject, not the IO. In some countries they say "pasarla bien/mal/etc.", but in Spain we say "pasarlo bien/mal/etc." (we refer to el rato, el tiempo, etc.). "Lo"/"la" does not refer to "cumpleaños", but to the time she enjoyed doing something. 
Todos sus amigos --- dieron muchos regalos.
so here m. regalos is OD and Olga is the OI. since regalos is already in the sentence then the answer should be le (for Olga).
le
--- compraron en diferentes tiendas especializadas del viejo San Juan.
here OD is regalos which is implied so the answer should be los.
Los
Por ejemplo, Paco --- compró una blusa de seda.
OI is missing so should be le
le
A Olga le gustó mucho la blusa y ella --- dio un beso a Paco.
'a' Paco - therefore OI - le
le
Mateo, el novio de Olga, también --- dio un regalo especial.
OI thus le
le
A nosotros Mateo --- dijo que iba a ser algo increíble, y realmente fue increíble.
stumped by this one. so mateo said blah blah 'to us' right? he bought something incredible which is the DO. so is a nosotros the OI and thus should we use OI since oD is stated so it should be 'nos'.
nos
i notice that my reasoning is matching the right answers. is this how one thinks to figure out the right answer?