How long is a piece of string?
How often you change coils is a personal taste thing. You'll notice a drop off in flavour and vapour production, when you change depends on how much you value those two really. Thicker and more colourful liquids tend to gunk up coils faster (this is by no means a scientific rule). On my setup, with cotton wick and a ~1.8ohm home rolled coil, I tend to rewire/wick every 4 or 5 days. I have gone as far as a week tbh, and on silica (I.E. what most shop bought atties use) 2 weeks isn't all that uncommon.
As for batteries, again it depends. The 650mah batteries I got for a small fortune from TotallyWicked lasted ages, over a year in serviceable life tbh, whereas a couple of my FastTech 1100mah cheapie batteries lasted a few months. They only got binned because of manufacturing crapness, like the threads being rubbish and the battery connector coming away from the tube more than the actual battery.