Is there a way to see how many cards are left in your library (besides counting)? Played Heedless Lash and nothing happened. 
On a related note, is there a way to see how many cards are in your hand when it is your turn (besides counting)?
Currently, there is no way to do either of these. The first one has been in the Suggestions pile for ages. I just added the second, as I also frequently find myself counting cards in hand.
Actually, there is a way to see how many cards a character has in their hand, though it doesn't work on the character's turn. On a character's section, you'll see a symbol of three yellow cards with a number on it; this tells you how many cards that character has in their hand.
Yes, but it is specifically DURING the turn that we were discussing. Say you're Haka, and you're considering whether you can kill something big with a Haka of Battle. Currently, it's tedious to do the counting if you have a big hand.
And Haka has two big hands.
That would be quite a nice addition to the game. Not 100% manditory, but would be nice.
I'd suggest putting that info on the menu that pops up when you double-click on your character card, maybe? On possibly on that line that says 'play a card' and 'use a power'.
I was just thinking, under The Multiverse, it'd also be good to have something that tells you how many of a given card are in a deck.
It already does. It is possible that this update happened in the MP Beta but it is/will be there!
Yep, that feature will be in the 1.5 update (both in-game and in the Multiverse screen).