I can't believe what I have read here.
3 Beeps is BAD. Bad bad bad. Bad.
Here is a list of the possible dash displays:
Jason Pearce | Chronicle - Audi Warning Lights and Indicators (ignore tyre pressure one).
Things that will cause three beeps - in my experience:
Coolant:
- Low fluid level - easy to check. Warning comes from the sensor on the header tank. Top up. Ignore - engine goes bang.
- High coolant temperature (Over 110 degrees) - easy to check. Monitor temperature gauge on the dash. Ignore - engine goes bang.
Oil:
- Low oil pressure - not easy to check. Can be the sensor on the right hand side of the oil filter housing. Ignore - engine goes bang.
Brakes:
- Low Brake Fluid level - easy to check. Top up. Ignore - crash into a wall.
These are the things that will give you 3 beep (Priority 1) warnings.
So....
You've check the oil level. Pointless to be fair as the S3 has a sump oil level sensor and this will tell you when the oil is low. This is a yellow (P2) warning.
Brake pads are also a yellow (P2) warning. This will have nothing to do with the P1 warning. At all.
The way I understand it is that you have checked the coolant level, and you have checked the brake fluid level and all is well.
If you are driving along and the temp gauge isn't going completely spastic (although you do have a CTS fault listed), and there isn't the sound of the engine actually boiling when you turn it off, then I'd be getting your oil pressure tested ASAFP.
Low oil pressure WILL NOT log a fault code.
Bottom line - priority 1 warnings are not to be ignored. They are there for your safety and for that of the engine.
Get your oil pressure tested (preferably tow it to the place doing it just in case), and get a new coolant temp sensor. Don't drive it again until the problem is solved.
Don't say you haven't been warned.