Come as you please! Remember it is outside and to maybe bring a jacket for the night if it gets cold but otherwise dress to the nines or as simple as you please.
If your invitation says "and guest" then yes, if not, we would prefer if it was just you.
We'd say thats up to you. For the ceremony it is in the grass so your heels may sink in a bit, but after the reception is on a deck so the choice is up to you!
You can find links on the Registry tab (click other registries to see links)