It depends which car parks, when and how 'intrusive' you will be (or how 'incognito' you will be).
The first one is the Arndale car park. You should be OK here, especially on a busy day like a Saturday.
The second would be shudehill interchange car park, accessed via a lift in the bus station IIRC.
It's not usually busy on the top level (When I went there anyway), so you will have to be more mindful. You are likely to be approached by security.
Tripods are likely to be a no if you ask, so only start setting up like that if you *really* need to. Otherwise just keep your camera on your strap and you should be fine.
If approached, say Hi, tell em your name, shake their hand maybe. Remember they're just doing a job, and toeing the company line of "Everyone's a terrorist or a competitor or up to no good".
Just explain you're visiting the city and you're an amateur photographer, and you're looking for good architectural angles for prints for your wall at home or something. It doesn't have to be true, just embellished a little to drive the point home you're just a photographer.
Say you've been to see x or x, is there anything he/she can recommend that's a must see?
They can ask you to leave, it's private property, simple as. They can make up whatever rules they want.
The key is to avoid having that thought enter their head
