It's a bit unclear on how damage works. Let's say I take 5 damage. There are two ways I can think of interpreting the rules.
A) I flip the 10,9,8,7, and 6 over. If this way then do the cards have to be in order?
B) I flip only the 10 over because that takes care of all the damage. Late game example would be flipping the 4 and 3 over because 4 isn't enough to cover the 5 damage. The order of the cards is obviously important.
The answer is A) and yes the 10 to 2 of hearts have to be in order.
Think of the top hearts card as being your hit points. You start with 10 hit points. When you take 5 damage you end up with 5 hit points (the 5 of hearts is on top). Yes, this is brutal. Yes, you die quick and often. And no, there is no 1 of hearts. When you go below 2 "hit points" you die.
But remember, if you take damage from a trap (diamonds) you only get hit once then you are done with that level. And you don't get the treasure.
If you take damage from a monster (spades) you keep drawing cards to attempt to defeat the monster until you defeat it or you die. Spades are far more nasty than diamonds. Though remember you can always drop a treasure card to get past the monster.
On a side note, I devised an "Easy Mode" variant in the variant forum you might want to check out. Basically when you play a card to defeat a monster and take damage, the monster takes the same amount of damage. So you only have to beat your last played card, not the original monster card. Makes the game far less brutal.