Thank you for the feedback!
To apply the health restoration, you must check the card's requirements. If they are not met, the effect will not be applied.
You can use money to purchase new cards. This introduces a choice in the game: do you become stronger in the current run or save up for new cards?
Enemy kills are merely a resource used during a run; there are no permanent upgrades associated with them at the moment.
Blast radius affects every weapon by altering the size of projectiles and the scope of explosions. I suggest using it with weapons that have a "radius" effect rather than with projectile weapons. :)
I don't want to give away too much about unlocking characters, but you'll need to collect something on the map. :)
Regarding progress, unfortunately, whenever I upload a patch to the browser version, it seems to get wiped out.
I'm addressing this issue. However, if you download the PC version, you won't encounter this problem, even if you download an updated version in the future.