You should have a 'key like ' shaft in your fob which may be a bit fiddly to extract. On the thumb side of the door handle, may be driver side, may be passenger side there is an in built panel which can be removed. Once removed there is a slot for fitting the fob tool in order to open the door.
This is how you entered a Hyundai i40, I imagine yours is the same. Reference to your handbook should give explicit instructions, if not call or visit your dealer.
Yes definitely. I think most batteries will last around three years, so it is a good idea to have it replaced every two years at service time. A good way to check it is to see how far away from the vehicle you can it to work. My car is only three months old, and I can activate the lock from 50 meters.
If you need to be right next to the car, get it changed asap.