This app was mentioned in 5 comments, with an average of 2.20 upvotes
https://play.google.com/store/apps/details?id=kr.core.technology.wifi.hotspot&hl=en
might not even need a root. I have been using this on various phones for a long time. I am currently with family mobile which also doesn't even offer hotspot yet this little app turns my phones hotspot on no problem. That being said its a phone by phone carrier by carrier thing. its tricking your phone into doing something its not supposed to do and some phones/carriers are to smart for it.
Yes. Typically, you can also set a limit on the number of connected devices and time out disconnect. Why not look at your current phone settings under Hotspot to get an idea. Or maybe you have an atypical phone? I've used cheap <$100 LG, Moto, ZTE phones.
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This is the app I used way back when I had problems with unlocked AT&T phones when the stock app didn't work. I still use it now.
https://play.google.com/store/apps/details?id=kr.core.technology.wifi.hotspot&hl=en_US
I used this app to get around Verizon blocking my hotspot usage on an old phone. Not sure if it'll work with your phone and carrier, but worth a try.
/r/GalaxyS3/ or r/ATT or r/StraightTalk would be a better place to ask this question.
Nope, check out Portable WiFi Hotspot