Most of the actual fixing of these issues happened in global chat, so for struggling mapmakers finding this forum later, I'll include a summary below.
I made territories thicker like:
1. Duplicate circle Ctrl+d
2. Select Circle1+Territory and click Path>Difference (this deleted circle1)
3. Select Circle2+Territory and click Path>Union (this made Circle2 into Territory)
I don't know how did those dots come there, but must be because of the circles.

Fix:
1. Select the path with the dots
2. Do the [Path > Break Apart] action (Ctrl + Shift + K) to split the territory border and the dots inside of it
3. Delete the unwanted dots
Oh sh*t I forgot, I have to rename all :( thanks
You can rename all the shapes at once:
1. Do Ctrl + F to open the search/replace panel (or open it via Edit > Find/Replace)
2. Set "Search in" to "Properties"
3. Make sure you have the right selection (in this specific case, "All" worked, but normally you want this to only apply to paths that are territories)
4. Enter the thing you want to replace and what to replace it for (note for any newbies: this can be used to rename all "path1234" to "Territory_1234" too)
5. Hit Find and confirm it located selected the correct objects
6. Hit Replace all