BMW 320i Engine Problems
BMW 320i engine fault
Take it to an independent mechanic who specializes in BMWs or European brands and have them assess the problem for you. The quote from the BMW dealer would suggest that they want to replace the gearbox, but an independent mechanic might be able to repair it at a much-reduced cost, and even if the gearbox does have to be replaced it will be cheaper.
Ask Smithy Xtra BMW 318 thirsty for oil
The PCV valve and the vacuum pump are the most likely causes of the high oil consumption, and although you say they have been done I would strongly suggest you recheck them. The pump in particular is a well-documented cause of oil leaks. I doubt changing oil would fix your problem.