Found Collection

 I'm not sure how I can apply putty to fill the gap and use surface
primer on it.

Depending on what kind of putty that you use... application varies a little.

epoxy: mix and stick'em on... some of them are soluable and
workable-without changing chemical property significantly-in acetone.  

putty: the tamiya putty works like just like many other type of putty
thingy: just plaster'em on, let 'em dry up a little and use them to avoid
drooling and globering, best of all you can mix with paint solvent of
some type-like gunje-sanyo's MR. Thinner-and fill up thin and shallow
seam line between glued parts.
I don't know much about polyester putty toomuch but they seem like
somewhere between epoxy and regular ones.

As for the primer issue... I don't know what material that you want to
use your primer and it probalby will take some experience and experiment
with various things, if you want to use air brush on plain plastic
(polyethlene), I don't see why you would want to use it unless you want
to cover up pores on parts with putty on...  
goo luck!