Free XBox Live Gold games?

As far as I understand, the great advantage of Xbox live gold is that you can play online. Now I have also read that you get 2 Xbox one games and 2 xbox 360 games per month. My question now is whether the selected games remain in my account forever or if they expire as soon as I cancel membership.

I don't know exactly, but yes I think they stayed. If you are interested in playing online, I recommend that you do not play on the XBOX but on the PC. You don't have to buy live gold and can still play online / multiplayer. You can also connect the controller to the PC, but only the One S controller, the older one (One) does not yet have Bluetooth

I mean you have it permanently when you activate it. If your membership expires, they will be saved until you reactivate the membership.

Yes, you can keep the games after your Xbox Live Gold subscription expires, whether on Xbox 360 or Xbox One.

Almost correct, see my answer.

You can also use the 360 games after the gold membership has expired.
The One games only as long as there's an active gold membership.

Great answer to a question about Xbox.