This really depends on what you think PVP is.
I have started in WoW, and I have quickly learned that PVPers there are usually a bunch of immature kids, they laugh at your attempts to learn PVP in battlegrounds and so on. They usually don’t need you, they don’t WANT you to be in their group, because you, as a newbie, slow them down and kill their performance (it’s short sighted but this is how it goes).
In EVE, we NEED you. Fights are asymmetrical, there is no battleground with 20 fixed players. If a new player does not join a fleet because he thinks he is new and not needed, it will be one ship less for that fleet - and it could be precisely that ship, YOUR ship that might’ve changed the outcome of the battle. This is why no one shoos away newbies from fleets (with few exceptions like capital fleet or black ops) and people typically do their best to explain to newbies what’s going on. And most importantly, your expected bad performance most likely does not kill the fleet. Yes you might lose a ship, but quite often it will be reimbursed by your corporation/alliance or your corp might already have some ships ready for you.
Also, in fleets you don’t fly alone, you have your fleetmates with you, and they are often flying against the similar mix of veterans and newbies
About your questions:
I don’t know a single alliance that would disallow their members to rat (shoot NPC piRATes) or mine. Typically a PVP alliance looks at the PVE activity as something to generate money for their members, with a silent hope that said money would be spend at least partially towards buying PVP ships. Specifically in nullsec, mining and ratting in systems increase their defensive index, which means the more people PVE in their own nullsec systems, the harder is to conquer those systems.
For PVE, you can do whatever you wish, sometimes alliance requires some modules for capital ships but you’re far from it. For PVP, usually DPS and logi (healer) ships are supposed to be of certain type and fit and there is a good reason for it which I can happily discuss at some point. However DPS and logi are not the only roles in the fleet and you can happily come in a random PVP fitted frigate or even a destroyer to many fleets. Just follow the basic fitting logic and it would work.
Also, since you like doing simulations, let me show you our lord and saviour Pyfa (download here)
(Btw good questions, keep asking, the only stupid question is the question that is never asked )