1. The map overlay doesn't always work, sometimes only in caves, I hope the end game always has map overlay.
Currently, it only works for randomly generated areas. But we're working on implementing it for all of them.

2. When I open the inventory and hover over a item it's not showing details, I have to click once to "activate" the comparison. This doesn't always happen
We're aware of this issue and we're working on it. Thanks!

3. During the beginning act when helping the men for the first time in the open world, the trees in the map are broken. I only see a slice of the tree hanging in the air and the rest is missing.
A screenshot would help to spot these trees, but we're going to take a look. Thank you!

4. The inventory doesn't show the weapon is a 1 hander or a 2 hander
That's not a bug, they have different name at the top right to dissociate them but currently no indication on either this is a 1 or 2 handed weapon. We received this feedback more than once though so we're already considering some changes about this.