So I'm doing the DLC (map 1) and on the way to the Tanner I stop by the huntmaster
to take a nap. Bed says sleep and save yet his damn son kicked me out ( I want him
deleted ;) ).

It's Henry's bed at Gamekeeper Vostatek.

At Lower Semine Mill I can't sleep at all anymore.
The bed shows on the map and it says Sleep and Save, but E
doesn't do anything.

Potwierdzam, też nie mogę tam spać :-(

The Bohemian Mattress Report:

Tachov - both beds work
Trotzky Castle - Even after the events of the story and the bed not being yours anymore it still works
Troskowitz - Both beds work (second unregistered bed is behind the trader's property)
Zhelejov Wagoner's Inn - Works
Herbalist Bozhena's Hut - Works
Gamekeeper Varel - Works
Lower Semine Mill - Bed displays on map, it says Sleep and Save but E does nothing
Gamekeeper Vostatek - Bed displays on map, it says Sleep and Save but you get kicked out
Nomad Camp - works

I think that's all beds in the first map (tests done on an existing save)

I'll avoid spoilers here, for those who haven't made it this far...

Tested only 3 beds since my full game reinstall yesterday, Wagoners Inn and Tachov Blacksmith. Both of those work fine.

The 3rd one I just tested, I lost access to that bed prior to update 1.3, that was in Kuttenberg, where 'a certain lady is on-assignment'. I thought it was due to events in the story, but I was still getting instructions from the Innkeeper, telling me where my bed was. However, the door was locked, as was the main Tavern door if I arrived late at night.

Tested a few mins ago, that access has now been restored for me :-).