1) Probably not legally. The thing runs, assuming an antenna with 0db gain, 10 times the legal limit. Since they usually come with 6db gain antennas, that's 40 times the legal limit. Causing interference to a licensed service with a device like that isn't an "oops", it's a flagrant violation of law, and is usually dealt with quite severely, even for a first offense. (And if the interference causes an airliner crash [there's a precedent for this], you're liable - financially, as well as legally - for whatever ensues.
Yes, I now they sell these things all over the place.
2) Probably not unless you're prepared to run your phone connected to the mains at all times. Those things don't run on peanut power. (1,000mw output, at those frequencies, probably means something like 2-3 Amps of power drain, so your battery isn't going to last long. Even on a USB 2.0 charger, you won't get more than an hour or so starting with a fully charged battery.)
3) Assuming the device is connected by USB, if you use an OTG cable to connect it - maybe. It's PnP in Linux - whether it will install to Android is anyone's guess.
A much easier solution - unless you want to steal wifi from people all over 3 counties while you walk the streets - is to put up a repeater (which is just a router or wifi access point running slightly different firmware - DD-WRT will do it nicely.) If the router is one with 2 external antennas, and you run a Cantenna in one jack (and another similar setup at the other end), you should be good for a few km distance. Legally. (IIRC, the longest path done this way was over 300km.) And you're still walking around with a little cellphone with no external gadgets.