That's very sad and I'm sorry for your loss. It's hard losing a cat you've had for so very long, I know. I wouldn't rush into making any decisions about complaints just yet while feeling very emotional. I imagine the vet took the cat's age into account when making their recommendation. If it was a vet you've known and trusted in the past that makes it easier to have faith in their judgment. It is hard to make the decision to give permission for euthanasia and you always wonder whether you've done the right thing regardless of whether your cat has huge amounts of treatment and you wonder if you're just prolonging their suffering or you have your pet pts there and then, as in this case. Maybe it would have been kinder to you to take your cat home and think about things but it wouldn't have helped the cat if the cat was feeling so ill. Sorry I don't know the answer to your question about blood tests, but I think from my own experience of very sick old cats that if your cat is quite weak even taking blood can be an ordeal for it.