I'm new in tube amps and I've read a lot on what to do and what not to do. I've read that using new tubes that are not wore make the amp last longer. Does it means that playing with a bad tube can break my amp?
Depends on what you mean by bad tube. If you mean an old tube, then no, it can't break it, just make your amp sound bad, produce microphonic noise etc etc.... If you mean wrong voltage, wrong socket, wrong type etc, then yes, it can break your amp.
I've bought, sold, and traded more gear than I care to admit.
A power tube or a rectifier tube which fails and starts arcing can damage your amp. That's a catastrophic failure though, and it can happen with either a new or an old tube. It's also not terribly likely.

So to answer your question, your amp won't be damaged by using an old tube, but it can be damaged by a tube failing- which old ones are more likely to do.
Ok thanks I was talking about an old tube. But what is a tube that is arcing?? How can I know if a tube is arcing?
If a power tube shorts, your amp will stop working. Arcing can only be diagnosed by opening up the amp, which I would not suggest that you do. It's not really something to worry about, since it can happen with any tube at any time, and if it does happen you'll know it because the amp stops working.