Yes, more pics would help. From what I can tell these are early 70's and might be a B303 model (pictured). Pictures of the inside of the drums would also help (some have african mahogany inside, others birch), as well as a pic of the single lugs on the floor tom. This pic is from Vintage Drum Guide, the sister site to VDF & there are lots of catalogues to browse. Premiers from this period are fantastic drums and your son is very lucky to inherit these, though I'd suggest starting him out on something smaller in the meantime. My 7 year old daughter has a kit with a 16" bass drum and she only recently started to reach the pedals properly.As for logos for a bass drum front head (reso head), I'd buy a white single ply coated head (like a Remo Ambassador for example) and by a sticker logo off of ebay. Here's one: https://www.ebay.com/itm/Premier-Drums-vintage-logo-7-X-2-5-Black-logo-sticker-decal-bass-drum-/151467789113Also, the tom showing in the pic is upside down.
Welcome to VDF.
This post covers everything, pretty much. I have a very similar kit, same finish. Like others have said, you have a very cool kit there. 1970's Premier drums, especially early to mid 70's, are their best, imo. The African Mahogany shells are super nice (my favorite of all vintage shells).
If you're up to it, I'd suggest doing a strip down, cleaning, waxing the shells (in and out), some new heads, ones that best suit the drums, etc. Premier has the best chrome-period. They owned the factory that did Rolls Royce's chrome. Once cleaned, it'll look like a million bucks.
I've attached a few pictures I've kept, from one of the Premier Facebook groups I belong to. Gives you an idea what they can look like, after some TLC.
Cheers.