Trigger is right. Heat mat needs to be encased. Electric in-floor heating is very safe, so I wouldn't be concerned about a fire hazard, but a lot of things in these pictures make me concerned about the heat/tile failing. They likely thought the amount of self-leveller they had budgeted would be enough to account for the wonky floor, but it looks like that was not the case, and now the tile setter is doing a poor job of accounting for the imperfections in the floor by putting thinset in in spots. Porcelain tile is not necessarily fragile (it takes a lot of focused pressure to make it break), but I would be concerned about the tiles breaking under weight as you mentioned, especially with gaps of that size around the perimeter of the tiles. With appliances and furniture on it. If you can hear hollow spots when you tap a tile with a broom handle, it means there are significant voids under the tiles, which will mean uneven heat transfer and risk of tiles breaking.
I also notice a few other things that tell me the installer was struggling to even get to this level of installation. The self leveller or floor patch looks like it was unevenly mixed. It looks like they don't have much experience mixing this product, or they didnt care to measure the parts/mix it thoroughly. Laso the wire has not been floated over properly, to protect it from getting damaged by trowels or traffic. I would check the resistance of the heating with a multimeter if it hasnt been done already, to make sure it hasn't already been messed up. Also in a job this size, it's unusual to leave out the perimeter tiles, unless you were having a hard time with installing the tiles in the center. When using levelling clips, you should at least put the clips in around the perimeter, so that when you add-on to what's already been set, you can still use the levelling clips. They cant use levelling clips on the perimeter tiles now, becuase the thinset will have set underneath the tiles, and they can put clips in.
These might be nitpicky points, but they are things that I don't do. Good luck with the rest!