A gas BBQ won't work at all.
While I don't consider a camp fire or a BBQ grill a good idea for annealing or hardening -
Heating the blade to non-magnetic, and then watching it cool, as soon as it looks black ( no red glow), quenching it in oil should soften it enough to work with files and sandpaper.
To make a charcoal BBQ grill work, you need a hot fire. Open the vents all the way and put a good stack of hardwood charcoal on (Not briquettes). Get it burning nice and hot, and if needed, use a home made blower ( hair dryer and 24" piece of pipe). Test the steel with a magnet, and when it does not stick anymore, heat for a few more minutes, then quench in the oil. You will need a pair of tongs of some sort. The extra long needle nose pliers from HF work pretty good for this.
For hardening, I do not suggest a fire pit or BBQ for the heat source.
Filling out your profile might get an offer from someone nearby to come over and anneal your files in a proper forge or oven.