https://www.backyardchickens.com/threads/geese-sticky-topics-index.497391/
This page ^ has some really useful links that address the basics of goose husbandry if you care to peruse.
I like Chinese geese, they get the reputation for being a bit louder and more temperamental than the other types of geese but they can be very personable and friendly. Their knobs can be sensitive to frost bite if you live in an area that gets bad windchill in the winter. A shelter may help prevent that.
As for food, most people use a flock raiser or similar poultry starter feed. Brewers yeast or Nutritional yeast can be added (like a tablespoon or so per feeding) and mixed into the feed for Niacin.
Geese can be kept with chickens in a coop / barn situation. I did it for a while, but eventually I decided to separate as the geese are very territorial when nesting and if they are sharing a nest area with chickens then you will have lots of featherless chickens. They will graze with chickens just fine usually provided ample range.
Regarding the baby pool, I think that is mostly up to you. How often do you want to dump and refill it, or move it, or clean the poop sludge out? I give mine access to a pond daily, but in their pasture I only keep buckets of water they can dunk head in but not swim in to prevent wastage. They poop pretty much immediately upon entering the baby pool so I never liked how often I’d be dumping the pool.
That said, any size kid pool will be enjoyed by the geese I am sure.
As for the heat plate, I’d say that if you have goslings that are only a day old or so then yes a brooder with heat lamp or similar source would be needed, especially at night.