I would cover them and keep them covered.

No rush to plant them out-mine don't got out until early July!

Can't comment on when to raise the mesh-I just lift it when needed, I don't have the time/flexibility to base it around when it's raining!! I suffered a bit this year but that was my fault for being lax over pegging down the mesh.

Sorry that’s incorrect they’ve put on some growth since I last looked

You could try breaking the rat tunnel up - maybe they'll move elsewhere. If the asparagus is attracting them, moving it to a metal raised bed probably won't stop them getting to it.

Unfortunately given the weather this year I think you would have to assume that May is the same as March or April. I’m thinking that the bugs will follow the weather not the calendar. If it was me I would plant with mesh in place now. Good luck

It was a bit overcast first thing but now it's intermittent sun but no breeze to speak of, probably because since I got a weather vane mounted on the end of my greenhouse there hasn't been any!