If the AT&T unit is a 'combo' modem/wifi router, then a new laptop would be able to connect over the airwaves, up to about 150'.
You do not have to tell anyone about what devices you're using at your own Network.
It's yours and private.
A password implies encryption, which you should set up at home; for security.
(a bit complex to cover here, but post another Q and someone will help).
There will be no interference with either a wired computer you now have, or other wifi devices within that 150'. This 'open' wifi arrangement has security implications, which is a whole 'nother can of worms, but first things first.
If you travel with a wifi device, you can connect to any 'open' wifi network, but like your home 'open' network, it has security issues you'll need to consider.
Once at your destination, ask the desk if they have wifi & what type it is, and it's SSID (the name of the wifi network)
Some places have free, open wifi; others have encrypted and free (you'll need a password to get 'on' it); some places charge for accessing wifi (again, probably you'll need a 'password').
There are many aspects of using wifi, both at home and away that you need to know for your safety, but generally speaking, when using 'open' wifi means anyone can 'see' what you're doing, so always keep it casual browsing and no high value site work like banking, credit card, or Facebook or other places that require a 'log-in'.
Study up on how to secure your home wifi, and using wifi on the road; they are important.
**Special note: some places have wifi, but you need to agree to the 'terms of service' (kinda run of the mill stuff), BUT you must also "accept" the Certificate from the router, which means all traffic (including "Secure" SSL) can be read, copied, and snooped by that router: not a good thing at all. In that case NOTHING you do is private or secure. Here again, only casual work on the Internet in this situation.