How do I slow down the passing of time and what's the best/safest level to slow it down to? I ask because I seem to remember being told that it's best not to slow it down too much otherwise the game becomes unstable?

Something to do with a console command named "timescale". Google that and you may get recommendations. And yes, it can screw up your game if you're not careful.

The command to adjust time is set timescale to xx, where the default value of xx is 20. Setting it to (1) will cause time in the game world to progress at the same rate as time in the real world.

Setting it values below 1 will cause NPCs not to cross cell boundaries. Setting it to zero can cause the game to not load properly when you fast travel. Some mods may also not function properly if the timescale is set to non-default values.