Can't you play with an emulator on the phone? That's the way I played Tomb Raider and in my opinion it was a lot better than downloading the game from the play store. Emulators seem to have more freedom with the controls as you can make the controls as you want.
What do you mean by quality was bad ? most emulators allow you to increase the rendering resolution. If you're trying to play an emulated game on native resolution yeah it's going to look very bad.
I only use emulators to play games that I couldn't play otherwise. Mostly Nintendo games, since I don't own a single Nintendo console anymore.
It depends entirely on the particular model and not brand. You shouldn't ever really look at brands when buying smartphones, since you can often get a better phone for cheaper with lesser known brands.
The small screen size is a big turnoff but it does make me immediately think of people who have those giant phones now that almost are more like tablets. I do not think I would like one but they would be a lot better for gaming.