Think it depends on what type of nursery you're thinking of using. In my area, if you want to use a private nursery, very few places become available for 3 year olds because the vast majority of children stay at nursery from birth /1 until they start school. If you want to use a pre=school nursery, I'm not sure there is a waiting list so to speak - I think you had to apply here as if you were applying for a school place (i.e. everyone had the same chance without having to put your name down anywhere). Just give a few places a call and see what their policy is.
is it just to get the 15 free hours or do you need it for longer childcare hours? With my 2, I had to apply just after they turned 2 as applications for the year ahead had to be in for the february regardless of when abouts in the year they would start (my 2 had october and november birthdays) - mine went to state run nurseries just for their funded hours.
Check your local authority website as it should tell you about the application process
Chances are you can register now for a place in two years time without needing to take it sooner, but double check the T&C in case you get to the top of the waiting list sooner than you ideally want the place
Depends entirely on the demand for the nursery. Around where I live, two years would definitely not be too long, and may even not be long enough (I'm having to register at 20 weeks pregnant for a place well over a year away - two nurseries didn't have the days I needed even at this stage!) Places can be harder to come by for older children as many of the ones who started as babies will be continuing. The larger "chain" nurseries seem to have more flexibility than the smaller independent or family-run ones.
I would definitely at least make contact with your preferred nurseries now.