One note on movement. I've always ruled it as 1" (or larger) increments, there's no subdividing the "move cost per inch".
You pay for the first 1" of movement, regardless of how far you actually go. If you only go 0.5", you still paid 1" to move. If you move 0.99", you pay 1" to move that far. This doesn't usually matter for too much, but I would apply it to level changes as well, or terrain costs.
If you move through a half inch of Woods and a half inch of clear, you pay 1" for the moving 1" +1" for the Woods. It cost you 2", not 1.5".
If you move up a half inch level change, you pay 2" for the level change.
You never pay less than the "move cost per inch", even if you move less than 1". You effectively pre-pay for each inch of move, then use it.
Fortunately, minimum movement takes care of a lot of these. If you are moving underwater at depth 2+", you use minimum movement and move 2". You don't have to go, I only have 6" Move, it costs 7" to move through depth 2" water, so I move 6/7ths of an inch..
But I wouldn't let somebody move some fraction of an inch through woods at the end of their movement either. If there's 4" of Woods (costs 2" per inch) that's 1" away from their starting location, and they have 6" of movement. They move the 1" in clear, pay 1" Move and have 5" Move remaining. They move 2" through woods, paying 2" per inch so 4" of Move, and have 1" Move remaining. They can't use that to move a half inch in the Woods. They have to pay the full "move per inch" cost, not a fraction of it.
I don't think we've ever made a ruling on that specifically, or how other people play it. But IMO, we don't want fractional inch movement in Alpha Strike (no 6/7ths of an inch in depth 2" water..). Curious how everybody else does it?