We need at least some measurements and you best check with your HOA if you can do this there are always many rules as for enclosing the breezeway before i would worry about that i would be looking at the floor plan . That is a long walk from the garage to the kitchen through the LR and as for a chefs kitchen no one I know who loves to cook would have a cooktop in an island with no proper ventilation to the outside in the shortest run possible . A game room on the same floor as the MBR I hope you have no kids because that is who would use that space at night .These are just some things I notice. Most breezeways I have seen are too small to actually have furniture but they do make sense to have them enclosed your only problem is that most of the windows in the study will then look out into a covered and enclosed space , this breezeway looks to be a decent size so maybe a great seating are to use for 3 seasons this is a pretty idea IMO the main floor plan needs some tweaking in order to actually use the lanai since that is the entry to the house from the garage