ᐅ Sealing connection joints in a prefabricated garage with a side entrance door

Hello everyone, we have received a precast concrete garage that was installed about 3-4cm (1-1.5 inches) away from the house. In this context, I have some questions where I need help.

• The roofer wants to seal the gap to the roof either with a waterproof membrane and an aluminum trim or with metal flashing. We are currently leaning towards the second option for aesthetic reasons. Would the first option be better?
• We would like to close vertical gaps between the house and the garden at the front and back of the garage. I still have two clamping strips left over that would fit at the back, because the garage is flush there. However, the clamps are missing. I also need a corner profile for the front. Where can I get something like this, or what keywords should I look for in the hardware store? Or what alternatives are there?
• What is the best way to close the gaps near the side entrance door?
• And how should I best seal the door threshold? Can I simply fill it with gravel and then place paving stones on top? This way, water could drain away if needed. Would an expansion joint be necessary then? Or would a different solution be better?

Many thanks in advance

So, we have now sealed the exterior. How would you finish the opening around the passage door and make the threshold flush?