Hip roof absolutely wants my wife [...] for the carport we already have a flat roof in mind but we are not sure if it all fits together
You can also overdo the hip roof: I would only put the hip roof over the main building body, check if the headroom works out, just extend the roof over the stairwell projection, convert the terrace roof into a shed roof, and do the same for the carport roof (in the area of the cars then as a gable roof with a ridge between the cars).
The window arrangement seems quite well balanced to me; in my opinion, it would only be different otherwise.
I know, hip roof is currently hot crap (for whatever reason)
In my youth, the disco mice were crazy about Asbach Cola. The hip roof is, in a way, the pageboy haircut for the house. The glass bricks from fifty years ago were "worse," and I find hip roofs, even if slightly overdosed if necessary, still a nicer sight than the smoky eyes that always give the substitute villas that lascivious-knockabout "something" *LOL*