Swollen trackpad

Swollen batteries are a serious issue. Yes, it's possible it can start a fire; how probable that is is anybody's guess.

Shut the Mac down and get it to an Apple Store asap. This is not something you want to try and fix yourself.

As to handling a fire hazard, I naturally tend to be overly cautious. If it were me, I'd put it in a vented metal box, an old loosely built tool box would likely do, but that's just me, and keep a close eye on it.

I'm sure others will respond with good suggestions.

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If the external device has a swollen battery, and it's not replaceable, my advice is to recycle it as described in the accompanying literature and buy a new unit.