1. Yes, a transition is required for laminate where it meets the marble threshold. You can butt solid wood or engineered wood (glue or nail down, not floated). But not laminate. In my opinion, the transition could have been extended under the door casing. As FloorMaven points out, this requires a little creativity (like cutting the vertical part off the molding where it goes under the casing so you can slide it under). It's not done "wrongly", but it can be done better. The bargain installer does work like you have. No one wants to pay the really good guy price (well, they do though, that's what we do - but you get what I mean).
2. The exterior door is done correctly, but with the same comment as for the bath. Part of the problem is it appears a thicker floor was once installed that has now been removed, causing the door casings to be higher than the floor. The floor installer is not responsible for the higher door casings. I know someone said they didn't like quarter rounds, but I don't mind them your particular situation. Judgement call.
3. Where the transition meets the carpet, if this door opening is less than 7', then this join should not exist. Moldings typically come just under 8' in length, so any opening less than that size should be done with one piece of molding. If the opening is larger, then there is no choice but to have a join. Again, not technically wrong, but you can see the join FloorMaven demonstrates looks better. However, it is glued in to a flat floor. Some transitions are designed to be inserted into a track and are removable. This type of molding has a little "give" when the carpet pushes against it, so the incongruity may be nothing the installer can address without changing how the molding was designed to be installed. There is also a little adhesive evident in your join, which should not be visible.
Hope this helps.
Thank you very much for your expert opinion and advice. Very much appreciated. )