Brown foamy sludge build-up in oil dipstick tube. Is this something I can remove and clean myself? Am somewhat mechanically inclined.

Transmission fluid (ATF), like engine oil, should be checked regularly. The transmission box has a dipstick, like the engine. To check the ATF level, firstly locate the dipstick which is in the engine compartment. You will see the tube which carries the dipstick runs at an angle to the transmission box as opposed to the engine oil dipstick which runs almost directly down.
Checking the level involves starting the car and while the engine is running with the selector lever in P (Park) remove the dipstick, wipe it clean, then push it back and remove it again. Now you can check the level. Fluid is usually added into the dipstick tube.
If you are losing ATF, check for leaks because the A/T usually does not consume ATF.

If the oil level (checked with the dipstick) is VERY high, and the oi on the dipstick looks like chocolate milk (or just after running, foamy chocolate milk), this usually means either the head gasket is blown, or the cylinder head or the engine block is cracked, allowing the engine coolant to mix with the engine oil.

No--- your done

You removed the air conditioning hoses or tubing
at the condensor or something & lost all refrigerant
& some green pag oil

I would not worry till after the foam gets heavier and more frequent, then you may have a head gasket leaking. If you change your oil and check the level in the morning and there is still a foam on the dipstick I would monitor it frequently for excessive foam or swhite sludge, then worry about a leak.

You may have sludge in the "pickup tube" which would prevent oil from circulating through the oil pump into the motor. Remove the oil pan and inspect and use a long piece of weed trimmer line to unclog if the tube has any nasty sludge in it. Do NOT alter the length of the tube. Make sure to remove any sludge build up in the pan.

Have the oil and filter changed,use 5w30w oil,and run it awhile,it may take awhile to get the lifters to prime up.

My 2005 A4 3.0 convertible audi is not a diesel, but I had a similar experience with a low oil signal going on and after checking the oil, which was sufficient, and replacing the dipstick, the light did not come back on until a subsequent trip. The light usualIy went on when I was close to the needing an oil change. I've had the car, a used one, for about two years, and the oil light minimum signal started behaving like yours early. About a week ago the oil pressure warning light came on. I don't know if there's a relationship, but if there is be careful. Audis of our vintage have a problem with sludge build up that damages the oil pump, which is a costly item. If you drive the car with low oil pressure you may seriously/fatally damage the car. I don't know if the sludge, if that's what you have, can be cleaned out, but I'd do it if it can be. My mechanic advised me to trade the car to a dealer rather than fix it. Hope you have better luck!

need to find out the pressure the pump is putting out hook up a mechanical pressure gauge most use the sensor port to hook into and test pressure if pressure good than u may have a sludge problem where a flush might help-if pressure low possible clogging [sludge build up] of oil screen-[which a flush or back blow-compressed air -to clear or clean pick up tube and screen should help ]--or internal engine problem or oil pump bad

if yoiu have an oil pressure gauge is the pressure good? check the pressure and also cjeck the thermostat and water pump those are major causes of overheating if you have water in your oil ( check dipstick for 9oil and if its foamy and light brown you have a head gasket problem if not its something else of what Imentioned)

are you sure its oil in the antifreeze? oil is brown. your van should have dexcool wich is orange, not green.(looks red sometimes)check the coolant again and check the oil. if it looks milky or foamy, there is coolant in it. sounds like it may be a blown head gasket. not good. stop driving it if you want to save your engine. you need to replace the head gasket/s, and flush the cooling system.