I don't know if it's legal or if it is then is it allowed to use in a game.
I have thought about it, as I'm designing things for 3d printing and couldn't reason £80 for a grenade.
Impact version is easier to make but timed is not that hard either if you have lathe. It's just the timing precision that's not easy to do.
I don't really like the impact bfg with that weight pushing the pin. It doesn't go off on soft ground. The tornado's impact is much more reliable I think but way too complicated to set it.
The timed ones all work on the same principle: there is a piston that has a spring in it and it moves in a cylinder that only has a tiny hole to allow air in or gas out. This way the piston moves slowly when the pin releases it, and when it reaches the end of the cylinder, and slams into the primer or just allows the rest of the gas escape instantly. The problem here is that timing depends on the lubrication of the piston, the temperature, the dirt, etc.
Custom mechanic timer would be too complicated to make. Custom electric timer takes up lot of space with the batteries and is easily damaged.