Heat shrink is my go-to for permanent work. If it's really important, melt some solder on it, then heat shrink it.

As long as you’re not wiring up a bridge you should be fine

Stranded or solid wire?

Line man's splice https://www.youtube.com/watch?v=O-ymw7d_nYo

A name brand Wago would go a long way. They're quality connectors as long as the environment is appropriate