Okay I understand what's happening now. I probably have to sharpen the controls section on this page.
Holding spacebar is only for units with a 1-2 range listed in the range stat on the card (so this means dagger units).
Florina and Lyn get their 2 range by pressing the purple ability icon on the card. Almost every purple skill works like this where you have to click that icon on the card. It's a 1 time effect and then you have to buy an item to replenish it.
Sorry the game is little unclear atm, but I hope this explanation helps!
About the mute and spacebar. Keyboard events sadly trigger the button sometimes after pressing it. I'll try to fix this in 1.2! Thanks for the report!