You have a 4 yr old Greyhound that you have recently noticed has a firm hard mass, which doesn't seem to be connected to underlying tissue. Although later you post a picture and note there are multiple lumps. The dog has been losing weight which the Vet wasn't able to diagnose. Loss of weight is common with cancer. The dog has a good appetite and high energy level, where low energy levels usually are associated with cancer. Thus mixed physical signals: Loss of weight bad, high energy good.

Since the mass is hard and not spongy it's not likely to be a fatty tumor. It could be a possible cyst depending on how long it had been there before noticed. It could be a sarcoma such as Hemangiopericytoma- slow to spread but will eventually. The only way you will know for sure is to get the dog to a Vet and have the Vet send off needle aspirates for all the lumps to a pathology lab. If it's something like Hemangiopericytoma then surgery will be required to remove it. If it turns out to be a cyst(s) then it may be as simple as aspirating them, and then treating with antibiotics, or surgical removal. If a fatty tumor then unless it impeads the motion of the dog, they are left alone.

Given your Vet charges an outlandish amount for visits, you might want to ask your local ASPCA if there is a Vet that would charge a more reasonable rate.

Dogs do not get cancer by running into things. They get injured.

A dog can get cancer at any age. I've heard of Lymphoma cases for 1 yr old dogs.

Get the needle aspirates performed, and determine the nature of the tumors.