I would like to shoot back at EVE ships

Also I would like to collect the tears afterwards when I blow up an expensive supercap in orbit

Then, make our stay in a location mean something. One simple way would be to implement rent. If you're stationed in a EVE-owned planet, the owner gets rent for your stay there. EVE pilots would benefit directly from that, so make Dust mercs also have a reason to want to pay rent. Make it so EVE-owned planets can have training facilities built in there by EVE pilots so your passive SP gets a small boost, so let's say you get 1100 SP per hour instead of 1000. Make it so other EVE pilots can destroy that training facility, meaning it would need to be rebuilt.

PI
An industrial capsuleer might want to boost his PI output and so he can hire a Dust Merc to go planetside and mine, extract some more planetjuice.

This would be a high risk high reward kind of thing. The whole point in using a Merc is because there is a high possiblity he could die.

Missions

I want to be able to go up against waves of rogue drones planetside, when things get too out of hand or I just need a little help a capsuleer can warp into orbit, fight off the space rogue drones and then OB some rogue drones.

We can then share the bounties.

Walking in Stations

I can dream right?

Ask not how we can interact with the Eve players but why Eve players don't want to interact with us!

I would like capsuleers to own pc districts and build surface infrastructures while paying us to attack and defend. I'd like for pc battle timers to be set by how long jumps take, I'd like eve capsuleers to run the show so we can be mercs, for us to gain standings with eve player run corps but able to gain good standings with as many as we want, not confined.

Chances are you will never ever blow up a supercap - much less a cruiser. Supercaps range from 20b to 80b. Even expensive frigates can cost upwards of 20m.