To just have Peanut seen by the vet, no tests or bloodwork, it's about $65. Blood tests run around $150 or more each in my experience.
I've never even heard of a vet that will include any bloodwork in that $65 fee, that's just the basic checkup. A good vet will handle, weigh, and look over them at that price and some will include complementary nail trims and wing clipping in that. But really it's what they can provide for free, just their time. Tests cost them money to run as well, either the kit they use or the lab they ship it to.
Determining age is mostly a visual thing, I think, there isn't a test for that. I'm not sure but most of the time the vet looks at the bird and will try to ballpark the age (if there is no band.) It's not an exact science but they can give an estimate.
Bloodwork gets expensive in a hurry and I understand not wanting to have it done but with new birds it's very helpful. They are very good at hiding their symptoms and new birds even more so since they are in new (often frightening to them, at least a bit) surroundings with people they aren't necessarily at ease with. It's instinctive for them to hide their illness or pain so things can and do go unnoticed until it is too late.
But I do understand; money doesn't rain from the sky and it can be hard to get the cash if you aren't already in a financially stable situation. I'm a student myself, the smartest thing I did was start a "Vet Bills Savings Account," if I can put at least $20 per paycheck in there it does start to add up, eventually. If you can though, I personally would try to get some tests done eventually on them, especially if they have a mysterious history and past injuries.