Each module will have a fixed start and end date, and in between those the will be fixed dates for assignments to be handed in along the way, usually with either a final assignment or an exam at the very end. You can hand things in earlier than the deadline, but doing this a very long way in advance isn't necessarily a good idea because you'd miss out on the advice and support available around the time everyone else is doing the work (both from the module team and from your peers). An exam, obviously, can't be done early because it's on a specific date.
Also, even if you hand everything in early for one module, you won't get the results any earlier, because there will be fixed dates for this; and you won't be able to start your next module any earlier, because they start on fixed dates (usually October and sometimes February).
Many people do study at full-time pace with the OU - I usually suggest doing 60 credits (part-time pace) to start with, and then upping the pace if you find you can cope. If you do find you need to stick to 60 credits at a time, those extra couple of years will pass surprisingly quickly!