It doesn't have to be huge, or expensive. Here's a fire-resistant lockbox on Amazon for $20. There's a bigger version on that same page for $30.
If you want off-site storage, call some local banks and ask what their lowest rate is for a safe deposit box and how big the box is. Most are around 3x5x12", enough to pack a lot of negatives in. You can sometimes find smaller banks that will rent them for $40-50/yr, but pricing varies a lot. You can sometimes negotiate a lower rate if you pay multiple years in advance. Just make sure to pay the annual fee, or they'll seize the contents, obviously.
You can back up your scans for free on Google Drive or Dropbox, up to a certain storage limit.
I got one of these, at my school they can't look in anything closed unless it smells. Keep it in airtight containers inside this thing and you will be ok.
Or superglue a small piece of metal/plastic over the reset hole.
Don't take this the wrong way but did you have the balance connector plugged in? I see your balance block and there is no charring and the battery balance connector is melted. If you don't use the balance connector, you're going to have a bad time.
I store my lipos in fireproof safe boxes of double walled steel, and I charge either on a fireproof bag , or this stainless steel sheet you can buy for counter tops to put down hot pans, it's dimpled metal and will save your desk from stuff like solder, flaming lipos, etc. I also have a networked firealarm that automatically calls the fire dept and it's mounted above my lipo storage, and one of these on the wall. Make sure you get one rated for electrical fires.
My last precaution is to keep my lipos stored in two locations so if one goes off, they won't all go off. We need a good way to dispose of lipos you know? I have several that have ballooned up I need to throw away, but it seems dangerous to leave them in a trash can and it might cause a fire at the dump. I have them in a concrete fire safe until I can get around to hammering a nail through them in the drive way.