Is it possible to have MuseScore 1, 2, 3 and 4 on the same computer without issues?

Yes, they can be installed and running in parallel on the same computer without conflict. It is possible to have for example 1.x, 2.x, 3.x, 4.x and even a Development build.

There's one issue though: only the version installed last will get started when double-clicking a score file.