Eve Online - Alpha to Omega 2019 - Two Important Questions!

I'd say you can do one or the other. ie If you use the orca in place of the corps orcas, then you cannot reprocess for skunky. If you use only the corp orcas, then you can reprocess for skunky. Whatcha think?
eta:Will you be streaming anytime soon?

Buffs yes, Refining no.

If you went out to a friendly Corp as a neutral Or from another Corp and asked to get in the fleet and get buffs it's the same as using Pyro to buff Skunky. Also you can get reprocessing from a friendly Corp (as a neut) there is a cost but the benefit is still there. ( I've done it and ended up joining that Corp with an alt) So not cheating in my opinion. If you do any reprocessing for skunky do it at a 5-10 % charge. That's about what you would pay someone to do it for you. Bee safe and fly well.

if you're going to subject yourself to the misery of mining as an alpha character may as well get all the little advantages you can I guess. Why not just join a null sec corp and mine there if that's what you want to do? Way better profits to be made. High-sec mining sucks unless you want to just make isk AFK.