No wifi but a wifi hotspot

I stayed in a hotel over the weekend, and even though the cheapest hotel on the highway has free wi-fi, the Hilton*** wanted $13/night for *in-room* wi-fi. So I didn't get it and didn't even bring my laptop. No big deal. (And they had a computer in the lobby.) ***Where I had to stay because it was a family event.
However, in the room I got a notification on my Android phone that there was an ATT wifi hotpot, and indeed, I was able to use wi-fi on the phone, including googling and reading websites.
1) Does that imply if I had had the laptop with me, it would have worked too? Or are there stricter rules for a laptop than a phone?
2) Did I only get the notification because my cell phone is on the ATT network?
If I had a Verizon phone, I wouldn't have seen the notification??
3) OTOH, if it were a Verizon hot-spot, I wouldn't have gotten a notification about that???? Only those with Verizon phones?
4) When they say you don't have wi-fi in your room, can I assume that doesn't mean the signal isn't there, only that one needs a password, which they only give to those who pay? But if that's what it means, and I paid does that mean I could use my laptop in all the other bedrooms in the hotel? Or if it's unique to my room, does that mean that other people could come up to my room and use their laptops there with the code they gave me, at least one computer at a time, just because I paid?
5) It's the hotel that provided the hotspot, right? ATT didn't sneak it in. And they wouldn't charge for wi-fi in the room and then allow or provide a hotspot there for free.... unless they made some mistake, like they meant to put it on the floor my well-to-do brother stayed on, the one with the executive lounge. Any chance it was on my floor or in my room by mistake??
Thanks a lot for any help you can give.
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On 6/16/2015 5:52 PM, micky wrote:

If your laptop uses ATT at home I think you can connect using your att username and password. or you can use your phone as the "router"

Correct, you get the benefit from ATT.

Yes.

Yea, AFAIK you can share the password.

ATT has deals with some restaurants and hotels. Not sure who pays for what though. Many McDonalds let you connect automatically with your phone.
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micky wrote:

They don't have much security.
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Good point. I only looked at a couple wikipedia pages. It was easier to use one of the 3 Macs in the lobby, two to be used standing up and one to be used sitting down. So since my back hurts some times, I got a chair from the restaurant 30 feet away, at 4AM each of 2 nights. Next morning, they'd put the chair back. Using Safari, I checked Private Browsing, but one page I had been to was in the drop down list at the location box of sites that start with Nati, I think it was. I was finally sleepy and didnt' have enough time to run more experiements. I didn't do anything involving money or my personal life.
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