Hookworms.
There is no reason for a dog to be relegated to a lifetime of hookworms. Do the reading and the work to get rid of the hookworms.
Dental disease will cause heart disease and needs to be addressed.
As stated above, most greyhounds do not have issues with being under. Talk to the Vet about your concerns and then get the dental done. There are a variety of dental chews available, so I would pick a couple of different brands that you can afford and give the dog one a day. We use OraVet, Pedigree Dental Sticks, VirBac C.E.T. Chews, and Sam's brand. Most of them I order from Amazon.
Good luck.