This thing has a CVT (continuously variable transmission) doesn't it? In that case my already stretched guessing ability goes beyond the breaking point.
Your check engine light must have been on already - b/c it would be a very strange coincidence to suddenly end up with a P0172 code at the same time as the others. They're completely different kinds of problems. But the P0172 is the least of your problems.
Both P0700 and P0701 refer to transmission control issues which are not necessarily killers. You can get stuff like this from a chafed wire (though it can obviously be worse than that). As far as I know the P1882 is about a speed ratio problem - that the transmission and its output shaft aren't registering the same speed. As near as I can tell a common reason for this is a slipping belt (if its a CVT) - and that is bad. That is new transmission time. But even so, those speed signals still have to be registered by sensors and sent via wires. Those could be bad and are not disasters.
If the only person who has looked at it is your local mechanic then you might consider running it by someone else. The typical mechanic is not well versed in transmissions of any kind and this is especially so with CVTs (still guessing there). Normally I'd say take it to a dedicated transmission specialty shop for a full evaluation. But CVTs are relatively pretty uncommon and even a lot of transmission shops might not want to deal with them. So you might spend some time on the phone to see if any of the local shops in your area are well versed in the CVTs