1. Chevereto and the Installer supports 7.3
2. The fatal error you mention is a missing class in your PHP setup. It has nothing to with the version number.
Okay, by a missing class, you mean a standard library is missing? Can you post a list of the required ones? I seem to remember a 'requirements.txt' being around somewhere but I can't seem to find it.
The system pre-checks for the missing requirements, but if your server gives false positives then it is impossible that the system works as expected. You have to accept that there's little chance in that your server setup could be wrong, because the system indeed check for all the missing classes using the APIs provided by the language.
The problem is that servers aren't standard by any means and I've saw plenty cases of servers when reported classes are "enabled" but not "available". Sadly, this is something very common due to the varied types of server setups.