Mines the same as yours pretty much, as far as im aware in my research plenty of people have said the variator on the 1.8's goes that way because of the oil not circulating to it on start up, I do not know that for fact just something i read in multiple places.
Also with research the diesel noise is irritating but not a critical fault, infact a common problem with this engine.
Its involves a lot of work as its a partial strip down, it sits in an awkward spot, plus timing belt change would have to be done at the same time, all in all i'd say around £450 for labour and parts, (main part being labour) not a job for a DIY mechanic.
If you do decide to get it changed maintain high levels of oil close to max and check and top up regularly as that will prolong its the variators life.