To answer the original question; yes, we are in a genuine relegation battle.
Our aim, now, should be to finish 4th from bottom, and if we hit that spot before the end of the season, our aim should be to climb a few more places and take some pressure off.
To use an old saying, "goals win games", and we just don't score enough, nowhere near, and you can only get away with that if you are solid at the back and keeping clean sheets.
If we can make it to January, and not be too far adrift, AND do some astute business with signings (and leavings), we might be ok.
On paper, these players should be too good to be relegated, but watching us week in, week out, suggests otherwise.
A grim situation.