You need two...........no way around it they will want to be their own kind and will be lonely without.
Grass clippings are OK, but they need open space to graze on. If they are kept confined for hours the parasite build up will happen and make for poor grazing to no grazing.
Geese graze not forage, they dont like super tall old tough grass. They wont eat an entire area either (think selective eating some areas will grow tall while others are eaten short), they pick and chose spots to eat, tasting, tugging and testing for the best, softest, flavorful greens.
Yes geese can be raised around dogs. As you know not all dogs can trusted with geese though. We have three Great Pyrenees, and none of the geese pay them much attention. Our 3 year old male is found sleeping with the Sebastopols during the afternoon.
When geese are young they are prone to hawks, but by the end of the summer (for spring hatched goslings) they have grown enough to free range a backyard all day. Prior to that a fenced area with a top (netting or shade cloth or something) to protect from hawks is required.
Goslings NEED grass, they should never be kept inside in a brooder only 24/7. We turn all goslings out in daytime pens starting at 3 days old. they have unlimited mazuri starter waterfowl feed, water and all the grass they want. A dog house with bedding gives them rain shelter and they get put back in their stalls at night.