Two good problems here.

Problem 1 is tough because all three plausible plays have some merit. 13/8 7/3 is solid and makes two new points. The only downside is the back checkers haven't moved yet. The blitz with 7/3 6/1* might work. The split play with 24/20 8/3 gets your back men moving and leaves builders working on the 4-point and 5-point.

The split play is the most natural here, so that would be my pick over the board. The blitz isn't as strong as it looks because you don't have a direct shot at a second checker. The play making two points isn't bad, but I'd rather make one point and split my back men.

Problem 2 is just a tactic that looks strange the first time you see it. Some call it the 'action play', others the 'banana split'. Your position is pretty bad no matter what you do, so make a play that gives you the best chance of winning. If White enters with a 6 or a 5 and hits you, you're in bad shape, but if you just break a point behind him you're in bad shape anyway with no upside. If you hit and he dances your upside is huge.