What is this WiFi thing? Will this work?

I know this, but my old phone radio reciver broke cause it over worked it. No more internet .-.

It is very unusual. Wifi receiver and router are supposed to be able to run 24x7. So it doesn't happen very often. But still if you are concerned about that then you should turn off wifi when you are not using internet on other devices. These things could work but depends upon the compatibility.
In my opinion it was not that broke your old phone. Probably something else. Normally humidity, dust, overheating and mishandling damage the phone.

@argav83: yeah I always have. The guys at T-Mobile once they found out the problem, they said it was cause you can't use WiFi hotspot on your phone to power gaming counsels or you risk damaging it.
Which eventually my phone internet didn't work at all.
I don't want that to happen again especially when I wasn't even using the WiFi hotspot setting all day every day.

For high bandwidth online gaming you do need a wifi router. Phone's wifi device doesn't pack that much bandwidth to support hi-def games. But even that shouldn't damage the device. It'd probably just lag while you access the wifi. Inserting and exerting you sim too much isn't a good idea. These devices should work though. Check the comments section from where you are buying it online. Google it's reviews only then buy it if you really need to. I'd suggest getting an external connection and proper wifi router for gaming purposes.

@argav83: we've never used it for gaming. Just downloading stuff on the Xbox and my laptop and stuff similar.

Imo it shouldn't damage your phone if you are just using it for downloading. Wifi device inside you phone should have a capability and it should be able to handle thing inside that range but that's about it. At last it's all about devices config. Wireless signals can't damage devices. Devices would either support those signals or not. But getting a dedicated wifi router is fine also depend upon your requirement.