Results of the spraying toilet line.

About 2 weeks ago I posted here about the toilet line that sprayed water all over the powder room floor and the front hall next to it. (and it leaked into the basement. Good thing I was only out for 2 hours.)
The follow-up is that some of the tiles in the powder room and hall have come partly unstuck.
This is a mid-priced townhouse built in 1979. The floor tiles are pretty stiff. Does that mean they are not vinyl? Did they still use asphalt tile in 1978/9?
I presume underneath is plywood.
My first plan was to use a heat gun to warm the tile and the adhesive underneath, to lift up the tiles, let them cool, put on new mastic (whatever that is!), new stickum, and put them back down.
But I thought I should check with you first.
I also have 3 tiles near the front door that are chipped. Is that because I throw heavy wrenches etc onto the floor there, rather than walk them into the house?
I figured I would use the heat gun to remove some good tiles from the hall closet, where some are covered by boxes anyhow, and trade them with the ones that have little pieces missing. Is that a good plan?
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