We bought a pair of Shetland geese a few years back. Our intention was to sell on youngstock to nearby smallholders, a sort of swap ring to keep unrelated pairs for us all and to sell. That didn't work - we had been assured that they didn't fly - they did fly, some forever. We were also told we were unlikely to breed many successfully. However, in their first season, the goose Minerva laid ten eggs in a lovely straw nest in their garden shed home, and was guarded fiercely by Magnus the gander. Actually she laid more than that but we took some but discovered we didn't really like eating them, so left them in peace to hatch the rest. The result can be seen on our website - nine lovely fluffy ducklings with two so attentive parents. Beautiful and heartwarming to watch. No-one in our 'circle' had any to swap. Well one did but then she gave up and returned the gander she had from us. When that gander came home some months later, the rest of the family went crazy greeting him, the return of the wanderer. For anyone who thinks geese are not fully sentient that was an object-lesson!
Of the nine hatchlings, seven were male, two were female and we sold one of those. The returnee Malcolm was so well marked and was clearly madly in love with his sister Maisie that we kept those two. A friend killed five for us, with Mr F's help, but he found it truly traumatic so we came to the conclusion that we couldn't let them breed again because any offspring would have to be slaughtered. Muscoveys have beautiful angel wings, but white geese have even more beautiful and huge angel wings.
So now we have a family of four very closely attached geese. The ganders are a bit protective when the geese are nesting, and used to go for us (a gander hanging off your bum by a pair of molegrips really hurts!) and the dogs, but they don't do so now. One thing with geese is they really will take a telling - watching Mr F give them a tongue-lashing and their sorrowful and apologetic looks are hilarious.
They watch the wild geese fly over, and sometimes call to them, but clearly they prefer where they live. After all they have a flock each of hens and sheep to boss around.
Don't expect a whole load of eggs - they are very seasonal layers, and if you want your geese for meat, expect many objections from your community members. Ours live here with no duties at all, just to keep us entertained.
They sleep in a shed at night and are readily trained to go to bed on command (remember geese used to be walked a hundred miles to market at one time)
No answer to your question of how many geese to the acre. They certainly make some inroads into the grass here and they bath in the sheep's water which means a lot of changing (in spite of a pond plus a dog pool of fresh water) As with pigs, for us geese are too individual and full of character to kill for meat, but they do make good companions for a quiet chat