I hope I don't muddy the waters for you, but to me the answers to your questions aren't simple or straightforward.

1. The action is more akin to a fly rod being fast or slow, tip action or full flex, rather than being different weight rods suited to different sized fish. They are not at all comparable to the various line weights for fly rods. The 5:5 vs 7:3 action primarily tells you where the rod will bend, not so much on how much force is required to bend it or what size fish it can handle. The last two or three sections on all the tenkara rods are pretty soft. It's in the mid and butt sections where you really see the difference. To a large extent, the choice of action should be based on whether you like a faster rod or a slower rod. That said, the 5:5 rods I'm familiar with tend to be softer and would be my choice if I expected to catch 4" fish. The 7:3 rods tend to have more backbone, and MIGHT be my choice if I expected to catch 4 lb fish. Given a choice, I would not choose the same rod for both situations. My #1 choice for the 4 inchers would probably be the Tenkara USA 11' Iwana and for the 4 pounders the Tenkara USA 13.5' Amago (both are 6:4). The Fountainhead Stone Fly 11' (5:5) and 13' (7:3) rods, respectively, are also worthy of consideration for those two situations. Other considerations are how brushy or open the areas are where you'll be fishing. I generally use a longer rod if I can get away with it. For 4" fish in wide open rivers, the 13' Tenkara USA Ayu is fun, too. It's a very soft rod (and not a good choice for Czech nymphing).

When you get between the 4 inchers and 4 pounders, then action preferences, open vs brushy streams, size and weight of fly, frequency of fishing in a breeze, etc all become considerations in rod choice. On some level, that's all fine tuning, though. You could pick most of the rods for most of the uses and be very happy.

2. Much more suitable for dry fly fishing than Czech nymphing. The soft tip sections make it a bit harder to get good hooksets when fishing a team of heavy nymphs deep, particularly in current. Because of it's stiffness, the Backpacking Light Hane would be my first choice for Czech nymphing, but would be my last choice for dries or small unweighted wets. Second choice for Czech nymphing would probably be the Tenkara USA Yamame, which has great backbone, but still has a tip section a little soft for heavy nymphs. It would also be a reasonable choice for the 4 pounders, althought the two rods mentioned above would probably protect tippets a bit better. The Fountainhead rods seem to have slightly softer tips, and would not be my choice for Czech nymphing, but are fine with dries, unweighted wets and lightly weighted nymphs.

3. Choice of line is mostly matter of personal preference. I think level casts better if there is any breeze. A lot of people think furled turns over better. If you decide on level, though, by all means choose fluorocarbon rather than mono. I'm a strong advocate of hi-vis lines, in either level or furled, particularly if you are fishing wets or nymphs.

One rod or line to do it all is clearly a compromise. For an all around rod I generally suggest the 12' Iwana. For an all around line, the size 4 hi-vis fluorocarbon level line. As with any other type of fishing, though, ask 10 people and you'll get 10 different answers.