Is tea that has been out on air for long dangerous to drink

A rainbowy layer is almost certainly oil. (This is called thin-film diffraction.) Earl Grey uses oil of bergamot for flavoring, and likely cheap teas you've used have oil-based flavorings as well. It's not surprising that the oil eventually separates, and there's not really any way to avoid that without significantly modifying the tea, or using tea that doesn't have quite so much oil.

I would definitely expect the flavor to be stale after it's left for a while - aromatic compounds are by nature volatile, and they'll slowly escape. You might be able to prevent some loss of flavor by putting the tea in something airtight (preferably a completely full container, so there's not even air on the surface) and chilling it, but it's going to be a losing battle. You said the color was stale as well; I don't know exactly what processes would cause that, but in general, the only way you're going to be able to slow down any chemical processes is by chilling the tea.

In the end, the real answer is simply that it's best to drink fresh tea. Your time would probably be better spent getting to where you can make it quickly - for example, get an electric kettle that can rapidly boil a single cup worth of water.

You can't (or at least I can't) tell without a lot of experience with teas of that sort. Generally, a sufficiently fresh tea will have a decently strong fragrance when you smell the dry leaves. As it grows stale, the fragrance will be replaced gradually by mustiness. But which fragrance to expect varies dramatically by the tea. For instance, pan-fried greens like dragonwell (longjing) tend to smell vaguely nutty, while a sencha will smell more grassy. Dragonwell will also be more yellowish while the sencha will be more greenish. But these are two of many different varieties of green.

Also, there's a continuum of oxidation from green to black, so "too oxidized" is really a matter of taste. If you buy a Darjeeling (black), it'll tend to be lightly oxidized for a black tea; if your green is darker than that, maybe it shouldn't be called green.

I'm sure with appropriate analytical chemistry equipment you could determine some aspects of tea "quality"--but this would be complete overkill unless you're running a major tea business and you want to ensure quality. And even then, you'd probably be better off hiring a number of taste-testers.

There is one test (but it's not definitive): brew the tea, then leave the cup out for a day. If it doesn't get dramatically darker by the end of the day, it's already mostly oxidized.

In any case, if you like the tea, why do you care so much about the quality? You can find some outrageously expensive teas--I've noticed some South Korean greens in particular--that start getting into the price ranges of fine wines, but unless you're doing this to impress people, you're better off trying a variety of samples and then getting the one/ones you like. (Hopefully you won't find that you really like those South Korean greens....)