Thanks for bringing the issue with the input mapping to my attention - I had not managed to catch that until now. I'll work on a fix for the next update.
The wave indicator is actually going away except for the one initial battle that has two waves; a long time ago there was going to be more multi-wave fights but they're not really a thing anymore. The main menu continue / load button logic has been overhauled as well for the upcoming version.
Definitely agreed that AP cost should be in the ability preview.
As to the design issues you mentioned, I have a feeling that both will be alleviated once the game's difficulty is tuned more precisely - right now it is erring on the easy side to give people time to learn the systems, so some decisions are less weighty than they ought to be. For instance you can afford to let the enemy attack a few extra times until the XP Up slot comes, because normal enemies generally don't deal much damage; ideally the cost vs. benefit would not be so obvious. I'll keep your concern in mind - the idea of other clock effects is something I have prototyped and didn't include just because it was one mechanic too many, but as the game gets longer there may be room for it again.
Thanks again for your feedback! Hope you'll check out v0.2 - I should have it out in a week or so.