Low coolant light keeps coming on but coolant looks full

SOURCE: Coolant warning lights keeps coming on

Audi TT's only take G12 coolant (vw/audi propriatary formula) you can add some distilled water to the water level to prevent the light from coming on, but as you explained you keep adding fluid (of some kind) and the warning like returns. that's a little evident that you have a leak somewhere.

put some paper towels or something under your car when you park it for the evening. when you come out the next day, pull the car away from the spot and look at the paper towels. if they have orange drops, that's your G12 coolant leaking. like McMuff460 said, check all the clamps/hoses for signs of the leak. if you don't find anything i reccomend taking it to a shop for them to check out. Your water pump might be on it's way out.

Don't ever put any other fluid other than G12 coolant and distilled water into your car's coolant system. It will cause some major issues with seals, leaks, and cooling performance.

SOURCE: Coolant light on an AUDI TT 2000

It sounds like it is low on coolant. Coolant expands when it warms up so if it is just low enough to trip the switch when it is cold it will shut the light off when it warms up. You should be ok to just top it off but be sure that what you put in is compatible with what is in it. There must also be a leak somewhere in the system for you to have lost some to begin with. Depending on how many miles you have on the car it wouldn't hurt to have the cooling system flushed if it's never been done before. If you do get it flushed take it to the dealer to have it done. Explain to them the low coolant and have them check the system for leaks at the same time. Hope this helps

SOURCE: coolant in coolant reservoir did not fill low level in radiator

you must drain air out of system
so when engine is warmed up, just unscrew slightly the thermo time switch which is the highest sensor and unit in cooling system besides the reservoir, until alittle air releases then when antifreeze starts coming out then retighten to specs. BE VERY CAREFUL !!!! LOOSEN VERY SLOWLY AND NOT COMPLETELY REMOVE FOR THIS CAN CAUSE BURNS. MIGHT WANT TO USE A RAG AROUND SENSOR. If this doesnt solve it then make sure you have the correct rad. cap. Also that the filling hose is not clogged as well as the little port on radiator.

SOURCE: Audi A4 2.5 V6 TDI - Creamy grey coolant in expansion tank

Sounds like blown head gasket (or worse) still to me.
Remove oil filler cap and look for grey oil.
Never use water these days but special coolant. Water makes vapour spots and cause block cracks, worse then blown gaskets!!!
vapour does not cool very well.
Look like you have cracks already.
Take a compression test if possible. But might not show op at that temperature.
The gauge indication troubles me.

SOURCE: OIL SENSOR LIGHT ON 2001 Audi 2.8liter

It could simply be maybe the person changing your oil never reset the light? or you have a oil pressure sensor leaking or not working.
most of the time its someone never reset the oil change light. even before it goes on it goes by mileage, so maybe it didnt go off yet cause you cnahged it a tad early.so noone even tried to reset it.

I guess you could have an oil pressure problem, but thats going the extreme route.. but if nothing else shows that could be a problem.