My Audi Tip-tronic gearbox needs regular top ups and water for cooling engine has oil. Is the Transmission oil cooler replaceable if yes what is its estimated price. (ZAR)

This will depend on if the cooler is air cooled or water cooled. With water cooled setups, yes, you will probably need to replace it.
With Air cooled setups if oil is mixing with coolant the problem is somewhere else on the engine. The most likely place would be the head gasket.

RADIATOR
Removal
1. Disconnect battery ground cable.
2. Drain engine cooling system as described.
3. Remove engine air cleaner.
4. Remove upper radiator hose from water bypass tube.
5. Remove radiator overflow hose from radiator and fan shroud.
6. Remove transmission oil cooler line from oil cooler inlet fitting.
7. Remove nuts retaining A/C condenser core to the radiator.
8. Disconnect engine control sensor wiring from the auxiliary electric cooling fan motors and the CCRM.
9. Raise vehicle on hoist.
10. Remove splash shield from lower radiator support and front sub-frame.
11. Remove lower radiator hose from radiator.
12. Remove oil transmission cooler line from oil cooler outlet fitting on radiator.
13. Remove retaining screws for power steering/transaxle oil cooler and position cooler aside.
14. Support fan shroud, radiator and A/C condenser core with a suitable jackstand. Remove lower radiator
support.
15. Position jackstand aside and carefully remove radiator and fan shroud.
16. Remove two retaining bolts for fan shroud at top of radiator and remove fan shroud from radiator.
17. Remove upper radiator hose from radiator.
NOTE: Loosen transmission oil cooler lines while securely holding radiator
connector with a back-up wrench.
NOTE: Loosen transmission oil cooler lines while securely holding radiator
connector with a back-up wrench.
18. Remove the radiator.

RADIATOR
Removal
1. Disconnect battery ground cable.
2. Drain engine cooling system as described.
3. Remove engine air cleaner.
4. Remove upper radiator hose from water bypass tube.
5. Remove radiator overflow hose from radiator and fan shroud.
6. Remove transmission oil cooler line from oil cooler inlet fitting.
7. Remove nuts retaining A/C condenser core to the radiator.
8. Disconnect engine control sensor wiring from the auxiliary electric cooling fan motors and the CCRM.
9. Raise vehicle on hoist.
10. Remove splash shield from lower radiator support and front sub-frame.
11. Remove lower radiator hose from radiator.
12. Remove oil transmission cooler line from oil cooler outlet fitting on radiator.
13. Remove retaining screws for power steering/transaxle oil cooler and position cooler aside.
14. Support fan shroud, radiator and A/C condenser core with a suitable jackstand. Remove lower radiator
support.
15. Position jackstand aside and carefully remove radiator and fan shroud.
16. Remove two retaining bolts for fan shroud at top of radiator and remove fan shroud from radiator.
17. Remove upper radiator hose from radiator.
NOTE: Loosen transmission oil cooler lines while securely holding radiator
connector with a back-up wrench.
NOTE: Loosen transmission oil cooler lines while securely holding radiator
connector with a back-up wrench.
18. Remove Radiator

sounds like a blown head gasket or worse a cracked block, is the engine using lots of coolant ? if not get the cylinder compression checked as could indicate if problem lies with the block but to honest on this age vehicle unless able to carry out repairs yourself i'd trade it in for a newer vehicle

If you have a engine oil cooler then yes thats the problem,the only oil cooler you have is the transmission cooler which goes into the radiator.and the transmission fluid would be full of water,you will need a headgasket

If no external leak and the transmission fluid colour looks white, the problem belongs to the automatic gearbox oil cooler. The oil cooler has broke mixing the gearbox oil and coolant causing this milkshake. It's a small radiator core type oil / water heat exchanger. It is cracked inside and transmission oil is mixed with engine coolant. Because the transmission oil pressure is greater than engine coolant pressure, the transmission fluid level drops. See also the coolant colour inside recovery coolant reservoir inder bonnet! It could be like this:


The automatic gearbox oil cooler type oil / water heat exchanger (oil cooler):


In the picture above the transmission oil pan was removed for oil filter replacement.

If no external leak and the transmission fluid colour looks white, the problem belongs to the automatic gearbox oil cooler. The oil cooler has broke mixing the gearbox oil and coolant causing this milkshake. It's a small radiator core type oil / water heat exchanger. It is cracked inside and transmission oil is mixed with engine coolant. Because the transmission oil pressure is greater than engine coolant pressure, the transmission fluid level drops. See also the coolant colour inside recovery coolant reservoir inder bonnet! It could be like this:



The automatic gearbox oil cooler type oil / water heat exchanger (oil cooler):


(In the picture above the transmission oil pan was removed for oil filter replacement).

The transmission cooler is mounted either in front of the coolant radiator or it is part of it. The auto transmission oil comes from the gearbox (hot) via small pipes it is then passed through the cooler and back into the gearbox. If you have signs of oil around the front of the radiator then you need to get it looked at ASAP. If you loose too much fluid you will damage the transmission and if the cooler splits you may end up with engine coolant in the transmission oil (not good as it will screw up your transmission very quickly)

That is not true oil and water being mixed can come from many different places. Such as a bad radiator which would cause transmission oil to mix with the water also alot of audi's have a water cooled oil cooler which are a very common cause of oil being mixed with with water. These type of oil coolers are located under you oil filter. They have water lines hooked to them which cools the oil and when they go bad the water and oil will mix. So dont be convinced that its your head gaskets it could be but not as likely. You can pressure test your oil cooler to see if this is the problem just romove it an plug one off the inlet or with rubber plug which can be purchased at you local hardware store (I found mine at ace hardware in there specialty drawers where they have all there bolts) then attach a air hose to the other outlet pressureize the system and place it in a bucket of water. this should tell you if the oil cooler is bad but be careful not to ove3r pressureize the cooler this could damage it and caust it to leak. 15 to 30 psi should be plenty.

Well, I'm not sure. Try changing the gearbox oil and try again. I saw on the other postings that most Audi gearbox problems pointing to a gearbox swap can be solved through oil change. I just had mine changed and it has reduced sluggishness and shuddering at low temperatures (from cool engine). It's a special gearbox oil you need to get from Audi, by the way.