Arrangement of carport on a non-right-angled plot of land

I would honestly be reluctant to post the finished plan here in a public forum,

So, before we signed the notary contract, we marked the plot and cut out and moved placeholders. That is the first thing you should actually do: arrange the house and necessary building components such as carport, garage, terrace, hut, etc. on the plot. https://www.hausbau-forum.de/threads/leitfaden-zur-hausplanung-auf-dem-grundstueck.30891/ It was written several years ago, but much of it still applies. Only after that is the house and floor plan developed. Unless it is a 15-meter narrow plot, I would not place a carport right on the boundary but with some distance, so there is still room for plants, storage boxes, or a walkway. And then you look at it that way. So if you haven’t made any drawings yet, then get started! Whether it’s for us or for yourselves.

1. How can we solve the situation that the carport cannot be parallel to the house due to the plot? Does it perhaps make sense to adapt the carport to the obtuse angle here, or is such an approach rather uncommon?

What is common is pretty much irrelevant. What matters is good functionality. For an appealing aesthetic, appealing proportions and appropriate stylistic elements count. Whether the building structures stand parallel to each other or not is not a value in itself.

2. Should the carport be placed directly at the house or rather with some distance? Currently, we have planned a distance of 1.5m, but lately that seems clearly too much to me.

There is no "should" distance. The distance is determined, as already said, by function, proportion, and style.

3. The carport has a planned width of 4m. It is intended that there is also space for the garbage bins. Is the space sufficient for a normal VW station wagon? What would you recommend here?

Yes, that would be sufficient if no further functional requirements come in, such as bicycles, wheelbarrows, an angled driveway, etc. But without a plan, this is all just guessing. I could just as well ask if a 6mm haircut would be appropriate for me. What would the answer be worth without a picture of me?

"Wash me, but don't get me wet!" No plan, no help.

Maybe the OP is on a diet and doesn't want cookies from Yvonne.

Ok, then straight from reality:

Our plot is on a very slight left curve - problem therefore identical. Carport is directly adjacent to the house or exactly at the property boundary.

Result: Carport is wider at the front than at the back.

My wife thinks it's great for parking...