No. Is that a common thing? Nobody I know has the same key for front and back doors. Our “back door” is a sliding patio door which doesn’t have an external lock at all, just an internal latch lock.
As for the key on the inside, I think that’s pretty common, at least in the UK.
Let me explain.
The front door closes and “locks” without a key; that is, you can’t open it from the outside if it slams shut. In this state, however, you CAN open it from the inside without a key, by turning the handle (i.e. pushing down on the horizontal lever).
To activate the deadlock, you lift the handle through 90 degrees, then return it to its horizontal position, and then turn the key in the lock - either on the inside or the outside, it doesn’t matter. Once this is done, you cannot open the door without the key: the door handle itself is locked in position.
We never used to lock the door with the key when we were inside the house, but a few years ago somebody broke in while we were asleep and stole a couple of bags from inside the hallway. Looking for car keys, I assume. Luckily they didn’t come upstairs and go for us.
Anyway, the policeman who came round when we reported it said this was a common problem with this type of lock, because you can reach through the letterbox and pull down on the door handle with a wire, and thus open the door. He said: always lift the handle and double lock it.
I am aware of the fire hazard situation, so we make sure there is a key stored close to the front door and easily accessible if we need it in a hurry.
Ironically, the break-in happened only a few months after we had this door fitted - the old door had been there for 30 years and consisted of a wooden frame surrounding a floor-to-ceiling pane of glass with no reinforcement whatsoever. Never had a problem at all (until a neighbour’s kid accidentally hit it with a football…)
