May I suggest a change in colour for each country? Turn Sweden yellow, Denmark red, Norway more strongly blue and Finland white. These are colours that the countries have in their national flags.
Flag colours were tried some time in the past. It looked fugly.
The idea was to go for cold colours, to give the map an "arctic" feel.
1) The river impassible is very hard to see and some of the mid area beveling looks like a river. If there is only one river based on the smaller legend, then you need to find another way to separate the smaller bonus areas. I don't have a current suggestion but a slight change in texture is something I'd try first.
Which beveling looks like river? I could try adjusting the bevel, perhaps a smaller & less opaque beveling might work. As for the actual river, I could try making it wider, but I fear this wouldn't look too good...
2) Due to placement of text, I can't tell if Askerhus is attached to Bohuslan. I would assum they are but I can't tell.
How is this not apparent? They are next to each other, there are no impassables between them. I can try to move the texts around a bit. There's not a lot of room though.
3) The dark blue text at the top (2 lines) and on the west (1 line) is on top of dark blue water and difficult to see
It doesn't matter, the same information is written in the top right corner.
4) I am not a fan of outlining in a fuzzy color, I'd rather have a full color for the countries. Unless the grey in the middle of each bonus area means something.
It represents snow... well, kinda. It's actually white but the texture makes it look a bit grey. It is there to make the bonus areas easy to tell from each other, while using the same colour for each country. If I used full colours, you could only tell where bonus areas end by the beveling, and if I need to adjust the bevel it will be even harder (impossible even). Then again if I use different colours for each bonus region, it would be hard for someone who doesn't know the geography of the area to know which country is which (and this must be known because the countries give a higher bonus if held alltogether).
If you have a solution for this dilemma I'm willing to give it a try, but it better not involve huge walls of text...