How many evolutions can be done in 30 minutes

Depends on how fast the game runs on your phone, but following this video

20 seconds for the evolution animation

6 seconds if it's new and being registered to pokedex

And some time inbetween. If we say you're fast and can get to the next one in on average 6 seconds (I assume many of them would be the same, ie. pidgeys)

If we then assume the pokedex wont be a problem; 26 seconds each 30 minutes

That gives ~69 evolutions, provided it's the same for all pokemon.

Less if you gotta deal with the pokedex

One single evolution takes exactly(ish) 25 seconds for the animation to fully play out, meaning that you can't do anything during that time. So if we account for user speed we can estimate that you can do 2 a minute, meaning you would be able to do 60 evolution's in a 30 minute period.

Upward of 70, conventionally. More, with luck. With additional hardware, beyond 200.

As calculated in the other answers, yes, you can easily induce more than 60 evolutions in half an hour by simply focusing. I think I've gotten up to 71, this way. But that's not the maximum.

Restarting the app can be faster than the evolution animation. On a current-gen phone, on good internet, when the servers have a light load, you can exit the game and then get back through the log-in process in as little as half the time it takes to wait out an evolution. In this fashion, evolution sprees of more than 100 Pokémon are attested.

You can log in to the same account on more than one device to multithread your evolution sprees. In this way, the only cap on your evolutions-per-minute is how fast you can operate the game interfaces. I have personally operated three phones at once, moving through them in a repeating wave, and evolved more than 200 Pokemon in one half-hour.

You can, given the opportunity, also combine these two techniques. Sounds like a real chore to me, though.

Please note that undertaking these tactics is not strictly against the game's terms of service, but account sharing is, so it is naturally against the rules to enlist a friend to help you manage multiple devices (they could still loan you a device, though.) Whether or not these tactics qualify as cheats, however, is left to your sense of conscience. Most games with a multiplayer element will absolutely not permit multiple game sessions on one account, so it's not like it would be wierd to see an exploitative element in these methods.

Theoretically, a third-party program abusing the deobfuscated game API could evolve your entire inventory near-instantaneously, but doing so would absolutely not be permissable under the TOS. Regardless, a cheater can do up to 1000 (the maximum number of Pokémon you can hold, after bag upgrades) during the activation period of just one lucky egg, plus however many more his teleporting bot can catch before the half-hour is over.