Regional trains are suburban commuter trains, much like commuter trains in the major metropolitan areas of the US (like NJ Transit between NYC and NJ, Metrolink in the L.A. area, Caltrain in the SF Bay Peninsula, Metra Rail in Chicago), or even like subway trains, if you have ever traveled to large U.S. cities. Like the American equivalents, seats cannot be reserved. You just seat on seats that are available, and if they are all taken, you stand up, although it is extremely rare that you won’t be able to sit.
Regarding taxis (Uber does not operate in Italy), they are not likely to be standing outside the Mezzocorona station, which is a small town. You will be better off if you get off the train at Trento and take a taxi from there. The distance will be a bit longer, and therefore the fare higher, but the alternative could be standing at the Mezzocorona station with no hope to go further.
There might be taxi services you might be able to call. Try and search in the yellow pages below.
https://www.paginegialle.it/ricerca/Taxi/Mezzocorona?suggest=true
