Check your countries national electric code for what is safe and legal. I recommend consulting an electrician.

Keep in mind that if you have a house with two prong outlets, you may run into something called shared neutrals as well. Coming from someone who has the exact same issue as you.. I would do some research. This is more of a notice if you are doing the work yourself. You may find that many of the outlets share a neutral. GFCI on one outlet may trip something all the way across the house.. etc.

I re-ran many of our outlets, GFCI on some of them, but not on one's I care about.

I also recommend doing research on GFCI in general. GFCI is mechanical. It fails sometimes. It takes time (while brief) to interrupt that circuit. In many cases GFCI is up to code without a ground, and it works. But there is no true substitute to doing it the right way.

Safety could definitely be an issue here as well. Depending on age this could be knob and tube wiring which is unsafe and a pain to work with.

Bad idea. Ground it.

It's funny, my mother in law got this text, but I didn't. We both live in Norristown. We have an oil furnace anyway so electric usage is minimal. I think its like sub-1000 watts when heating?