About the vax issue: Adopt from individuals. A rescue or shelter probably vaxxed them already or will require it before they get adopted.
About registration: I think shelters will require it since they're operated by the city. Otherwise, I don't think you'll have to go through that process at the time of adoption.
About food: looking up online and find some recipes you like to make for your dog is probably the best way. Or there are some fresh (frozen/refrigerated) options but I'm sure they're pricier than making your own.
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