What if you put the battery in first on level 7 on questionaut

It makes no difference to the question setup. You have to throw the switch (lower left).
You have to do these 3 things in no particular order:
- Grab the battery and put it in the holder.
- Screw in the large light bulb at the top.
- Throw the switch to isolate just the top bulb.
This makes the top bulb bright and the mouse character comes out to sunbathe.