Most casinos claim to work on a phone; fewer are actually built for one. These are the sites with a dedicated app or a browser experience that holds up on a small screen, listed with the same licensing and payout information as everywhere else on this site.
Rarely. Most casinos run in a mobile browser, and an app is a convenience rather than a requirement. Where an app exists it is noted on the casino page.
It can be. Live dealer tables and newer slots are almost always available; a handful of older titles are still desktop only.