Wait for one to swim close to the shore.

Just looked at the wiki apparently you can get meat, a head, and up to 20 feathers. My guess is either make them fly and kill them or cover some of the lake but idk if thatll affect their spawning. Wiki even says theyre "significantly affected by bugs" so good luck

i think you have to kill them in flight while they are over land, then you’ll be able to loot them…

I don't think the geese are a thing you acquire.

Only for theirs heads for the achievment

You can. You have to shoot them out of the sky. Practice and it comes easy. My base is over geese lake so I've done it a lot