I have reposted your image with a small modification: I have circled in red the icons on each screenshot that answer your questions.
- terrain icons.jpg (306.51 KiB) Viewed 1768 times
Upper left: Close Terrain (from the thick forest), Blocks Supply (from the thick forest), Vulnerable Position (from the river). Vulnerable Position is the one that makes this a risky location. If you hover your mouse cursor over the icon, it will tell you that enemy units will get +4 attack and +4 defense when they attack this hex.
Upper right: High Ground (hills), Close Terrain (hills), Vulnerable Position (river).
Lower right: Vulnerable Position (river).
Lower left: Close Terrain (swamp), Vulnerable Position (swamp, river).
My understanding is that terrain modifiers don't stack with themselves. So that river swamp in image 3 won't be any worse than a river without a swamp or a swamp without a river. You don't get double Vulnerable Position, in other words.
Standing on a river in a forest won't "cancel out." You will be in close terrain because of the forest and in a vulnerable position because of the river. The close terrain can be advantageous (say, if your unit is infantry and the enemy attacker is a tank), but they'll still get bonuses to attack you because you're in the river.
The unit on the frozen river does indeed suffer from Vulnerable Position, as I remember it. I interpret this as the instability of ice and the ease with which an artillery barrage might shatter that ice.
