Hey
I moved here last month and I left my dog at my country. I asked some of your questions to many people and heard many different answers. I know taze bazar and I dont think so pets at there are vacined. 600 manat is madness. if you go there with any Azery he/she can buy them at least half of that price. But you should not appear around them when they make bargain.

Traveling with pet is changing airline by airline and of course which country you are traveling. I know that almost every airlline regulations said that pets (I mean dog especially) have to carry microchip that all information installed. And they should travel with box with a suitable size as well.
Azeries (may be 99 percent) are not living wtih pets in their home. They like dogs very much but just only in their garden not inside the living places. So you may bother your neighbors. especially if your pet is starting barking. I m not really sure of it.
Finally I m looking for good vet clinic too. I will go to Turkey to take back my dog at the end of next month. I have golden retriever a year old , Azer Airlines take 200 Manat for the carriage and I dont know how much I will pay at the custom. I ready to myself to paying small fortune as I use to pay almost everywhere in Baku

These are all I know.
So good luck I hope I can help you.
Aqu