Carport/Garage width - is 2.50 m enough or is that rather too narrow?

Is a boundary distance of 50 cm even permitted in RP? In Lower Saxony, that would not be allowed at all (for good reason, see Müllecke).

Slowly.
You are allowed to move closer even in Lower Saxony.
§ 5 Abs. 8, Satz 2, Nr. 1 NdsBauO.

Likewise in RP, § 8 Abs. 9, Satz 1, Nr. 1 Landesbauordnung RP.

Right up to the boundary. Facing the garage towards the boundary. That will also withstand the rustling of the plants.

Slowly. You are also allowed to set back in Lower Saxony. § 5 para. 8, sentence 2, no. 1 NdsBauO.

Yes. It says "Without distance or with a distance reduced to 1 m from the boundary, [garages] are permitted." So not with 0.5 m distance. But as I said, Lower Saxony. In Rhineland-Palatinate, it seems to be different indeed, after skimming through.

2 x no.

50 cm or 50.1 cm are "up to 1 m" (Nds.) - or analogous / textually a "reduced depth of the setback areas" (RP).

For RP here is § 8 para. 9 of the State Building Code in full:

(9) Opposite property boundaries, without setback areas or with a reduced depth of the setback areas
1. [I]garages,
2. buildings and installations for local supply with electricity, gas and water and
3. other buildings without habitable rooms and fireplaces
may be erected if they are on the property boundaries or at a distance of up to 3 m from the property boundaries
a) do not exceed an average wall height of 3.20 m above ground level,
b) do not exceed a length of 12 m at a property boundary and
c) have roofs that are inclined no more than 45° towards the property boundary; gables at the property boundary may not exceed a height of 4 m above ground level.
[/I]
All this is the privileged exception to the principle in paragraph 6:
"The depth of the setback area is 0.4 H, (...). In all cases, however, the depth of the setback area must be at least 3 m"

To exercise one's hammer-right on the mentioned wall on one's own property along a half meter strip of dirt while scratching one's back on bushes will bring no joy.

I then clearly "vote" for this proposal:

3) build a double carport with separate rear storage space (no garage, gain in driveway width by eliminating the garage wall)

50 cm or 50.1 cm are "up to 1 m" (Lower Saxony)

1 x No. is right. In Lower Saxony, the rule is: either build on the boundary or keep at least 1 m distance.

Right up to the boundary.

Even if it's allowed differently in Rhineland-Palatinate, I can only support that.

In the utility room is the ventilation grille (outlet) of the air-water heat pump (Stiebel Eltron LWZ304) facing the garage/carport.

It's a bit off-topic, but are you sure that's what you want? Is the planning final or can a split unit still be implemented that vents somewhat away? That would also alleviate the carport issue... I'm asking because we also have the aforementioned heat pump, but our technical room is in the basement. Due to the noise of the heat pump, I wouldn't want it on the ground floor. I think you will notice the humming during operation, or you should soundproof the utility room. We don't have a soundproof door to the technical room; you can clearly hear the pump with the door closed in the basement hallway in front of it, but practically not at all upstairs on the stairs on the ground floor.