WiFi and Hotspot are different as are the settings.
WiFi defaults to power saving on when you restart your phone. Setting from dial pad *#0011#, then select WiFi will allow you to toggle the default to off, but it won't stay that way when you restart the phone. You want the ON default to keep battery from being chewed up by the phone looking when there is nothing to find.
You can't use WiFi and Hotspot at the same time. Hotspot will turn off the WiFi, and you want that.
Hotspot:
Turn on Hotspot, then touch Mobil Hotspot. Only from that screen can you now touch your menu key. You'll see timeout settings. Select that from the 10 minute default to what you want. I selected Never.
Remember that your smart phone is a powerful tiny computer. It is a phone, texting thingie, internet thingie, camera, mp3 player, email thingie and all those many things it can do for you.
EACH OF THOSE MODES has it's own menu and settings, not just the basic settings feature of your tiny powerful computer in it's home screen mode. This is the key to getting your phone to do what you choose to have it do, not what the carrier or manufacturer thinks you will like or want.
I hope this helps someone.
-Eddie-
Houston Texas, formerly Sprint and now ATT with the Samsung Galaxy Note II