The answers to this question list mobile apps that presumably need Internet and are intended for use on small planes. I assume Cessnas and similar planes don't have satellite internet; how do these apps connect? They appear to be mostly used in Europe; do other countries besides the US allow cell phone use on planes?
To answer the question how do these apps connect?
I assume Cessnas and similar planes don't have satellite internet;
correct, at least not any of the Pipers/Cessnas I've flown but Cessna does make some stuff much larger than a 172 these days...
that presumably need Internet
This is incorrect, in the US and many other countries now where ADSB-Out is required for aircraft mobile apps can plot traffic as long as they connect to an ADSB-In unit. In the Piper I fly there are 2, the Garmin 650 Nav/Comm and a Sentry, both of which I can connect to my IPad and have it display traffic.
I personally use ForeFlight as my electronic flight bag, but there are others like Garmin Pilot all of which have off-line caching of charts/nav-data/information so that you don't need a connection to render anything. Pre-Loading required charts of an area is part of my preflight. ForeFlight offers both internet and ADSB traffic.
Also of note, while I wouldn't rely on it and it could be an issue to actually use your phone in flight, plenty of GA ops occur low enough to simply receive cell service.
"I assume Cessnas and similar planes don't have satellite internet"
It's not an issue for small single-engine planes anymore. You can get handheld satellite Wi-Fi hotspots (e.g. Iridium GO!) which work when placed on a glareshield or with a suction-cup windshield antenna.