Draining is not too difficult, my guide probably makes it look harder than it is, if you read and digest the steps in the guide you shouldn't have any problem (assuming your transmission is an 096), or print off that guide and get a mechanic to do it, it won't take more than an hour. You can get Valvoline MAXLife ATF (fully synthetic and conforms to DEXRON specifications) for £7/bottle so it is only going to set you back
The whining noise and slipping is also an indication that (amongst other things) the fluid is too low.
Re it allowing you to start in any gear as mentioned this will be an electronic problem and not solved by changing the fluid, you need to get the car on VAGCOM first and check all the measuring blocks and error codes first.
Good luck :)
