What chemical processes occur in tea that spoil it after some time?

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.

From a text published by the Royal Society of Chemistry on the matter [pdf], Dr Andrew Stapley writes that to brew for long periods

...introduces high molecular weight tannins which leave a bad aftertaste.

The lighter weight tannins provide the colour and flavour of the drink, and require the higher temperatures to infuse properly, but the heavier weighted ones seem to provide the undesirable taste.

I believe this is why microwaving tea also leads to poor results.

I hope I understood the problem and question correctly: As I got it you want to know why tea (in your example earl grey) turns dark, gets a skin on top and changes its taste after some time, is that right?

That's the same as brewed green tea turning brown after some time.

If so it has to do with oxidation of some stuff in the tea and can be prevented by adding something acidic like lemon juice, citric acid, Vitamin C powder or the like as antioxidant. If you add that after brewing the tea you will see a lightening of its colour. After than your problem should not occur any more or at least in very reduced amount.

I have found that a back stir after stirring the tea, always eliminates the sour taste and my tea last longer. If you understand how brewing works, (swirling) it makes sense. It's silly, but it works.

I, too, have been looking for the answer to the OP's question, which was not answered here, btw. I think the process he is referring to is the eventual growth of bacteria in warm tea, but I have yet to find the definitive statement from an official source. I have noticed it in brewed tea that has been sitting too long in restaurants before serving. I do note that the authorities are now recommending that people not make sun tea, and cite the growth of bacteria as the reason. My experience says that refrigeration is the answer to keeping the tea from growing this bacteria.

Also, and this rather mystifies me, some people seem not to be able to recognize the taste of tea that has "gone bad." Others, like the OP and I, recognize it instantly. Sometimes the bad tea has a slightly foamy or fermented look to it.