Yes. You wax ring has probably failed and water is getting under the vinyl. You will need a new floor and possibly subfloor replacement

What can I do in the mean time

Save up money. There is no way to stop the leak other than to pull the toilet and reset it. You can’t clean the stain because it’s in the vinyl but under the top clearcoat.

Can mold grow in those conditions?

Cause I think it’s making people in my house sick

If it is a leaking wax ring they are a cheap fix. You will have to pull the toilet but its not hard to do and then scrape off the old wax ring and replace with a new one. We always spend a little more for the double thick ones although last time we put reusable rubber ones on and no water leakage. It won’t fix your floor but if that’s the problem it should dry up over time.

Wood or concrete subfloor?

I doubt that the mold is making anyone sick. If it won't scrub off, then it is encapsulated under a clear coating of the vinyl. But it needs to be fixed promptly. If the subfloor is wood, then it needs to be fixed yesterday.

Yea the subfloor is wood

It could get very costly, if it isnt taken care of right away. As it is right now, the vinyl needs to be replaced for sure, but, you also could have a rotted floor under there, besides mold, if its been leaking a long while. Shut the water off, and flush the toilet, and remove the toilet. Cover the sewer opening, to prevent sewer gas escaping. and check it all out. The more you use it, the more damage it causes, and the more money it will cost to repair it.