Of course you can. All propane cylinders have check valves to keep from leaking out when not in use. You would have more of a chance to leak, if it were attached to your stove. Just make sure to unscrew the tank from the adapter, too.

yep the stove did not have a tank on it when you bought it , right
how else are you going to change tanks ,

Yes. These types of fuel bottles are self-sealing. You don't have to wait for it to be empty before removing.

yes you can unscrew it and reuse it many times until its empty.

but, if you notice a hissing noise or an unusual smell coming from it, set it aside until its empty. that almost never happens (like once in a thousand).

Sure can -

Yes. Just make sure you totally take it off and totally screw it back on. The only time it can leak is if you leave it screwed on just enough to engage it. That being said, also make sure you don't over tighten it. Just hand tight till you feel some resistance. Be careful about crossing the threads. If you smell gas other than when you initially take it off/put it on/start it, you may have a leak -either from a bad seal, crossed threads, or a bad canister though this is rare.