GSM doesn't work after upgrade of IDE

Those are warnings, not errors. Errors are a problem that causes compilation to fail. Warnings are about things that don't cause a compilation failure but may or may not indicate a problem. The Arduino libraries used to have lots of these warnings that didn't actually cause any problems but were super annoying. They have fixed some of these recently but the GSM library hasn't been very actively developed. Note that you will only see these warnings when you have them enabled at File > Preferences > Compiler warnings so it's possible that they were also present in the Arduino IDE 1.7.10 but you just didn't have them enabled. Also note that with Arduino IDE 1.8.5 the compiled library is cached after the first compilation so you will only see the warnings on that first compilation. If you change library versions or otherwise modify the library or change the board selection the library is recompiled.

I don't have any experience using this library or the GSM Shield 2. Hopefully someone with more knowledge will chime in. It's possible that the problem is caused by a change in one of the other libraries that the GSM library uses. These appear to be all part of the Arduino AVR Boards core. So you can investigate this by repeating the process I described above, only by rolling back through the previous versions of Arduino AVR Boards via Tools > Board > Boards Manager.