>
here is not a question, the is being used as speculation, so it means something like "I thought he would..." or "I imagined he would..."
> I think that means the veterinary is going to do a proper surgery and he begins an incision, but I'm not sure about that construction's meaning.
That means "right there and then" and we're contrasting with the idea of , "proper surgery", before that, so it looks more like "While I was thinking that he would do a proper surgery, the vet cut (him) open there and then", in other words the speaker was expecting an operation done in the operating theatre with sterilized equipment and masks and things, but the vet just whipped out a scalpel and started cutting at the scene.