Welcome to the forums, Ronan265 and Budgie! Don't forget to tell us his name will you....unless of course it is Budgie
Windows really should be covered with something as budgies can cause themselves serious injury if they do happen to collide with them. I would look into perhaps some lacy net curtains which will allow daylight in but still give good coverage. Vertical or Venetian style blinds are also good if the budget or your living circumstances allow.
Often the most important part about teaching a bird to fly is teaching them how to stick the landing! You can start in a carpeted bedroom perhaps, standing maybe a foot away from a nice soft bed and giving a
very gentle boost, so that he learns how to land. You can do this around the house at various spots where he is authorised to land, such as the top of his cage or a playstand if he has one, and gradually increase the distance over time until he is confident with those landings. Then he will learn where is appropriate for him to land (not that he will necessarily stick with just those spots of course!), at the same time as building strength in those little wings.