Just my two cents, but I think for the most part your encounters were fine. You shouldn't worry about the first death in the least. The player felt comfortable dancing around with 10 hit points, and then got stomped down for it. As long as you don't punish players too much after they die (allow raise dead, new characters of a similar level...), they'll eventually learn to appreciate that you as a DM won't pull punches. They'll begin to work together more on a tactical level, and soon a player with fewer than 1/4 hit points will be treated as someone to protect and rally around. I regularly have monsters Coup De Grace PCs or usual brutal focus fire if it would be in their best interests, and it's forced my players to really pull together and think realistically about the threats they're facing.
As for the second encounter, while a lot of people say avoid domination and stuns, it was still a reasonably fair encounter with one exception, the fall. As a DM, you have to be really, really careful about any terrain piece that can kill a player outright, which that fall could. I think that was your only real mistake in design and it wasn't that terrible. It's a cool idea, but at your player's level, a forty or fifty foot tower is a little fairer, not nearly as deadly, and still invokes the same level of tactical thinking.
From what you've posted it appears that you and your players might still be kind of getting the hang of a few aspects of 4E. That's fine, that's one of my favorite parts of the new system. But sometime miscalculations might happen. In that case, consider either fudging a little (e.g. adjust the falling damage to that PC didn't outright die the second time), or perhaps even better, give your players a bit of a reset button to help them out. When my group was just learning the game, I gave them 5 miracle man chocolates which could raise the dead instantly. It gave the group a safety net for all the mistakes we made while new to the system, and kept the story moving along when those mistakes did happen.
Talk with your player, tell her it wasn't personal, and just let her know that sometimes that stuff happens in D&D. Next time it will be someone else. Hopefully your players are willing to suck up the occasional bad night or forgive you & the dice for unexpectedly difficult encounters. The fact that your group takes the time to sit down and talk about how to make the next gaming session go better, tells me this is probably true and that in the long run you guys will do just fine.
As for the second encounter, while a lot of people say avoid domination and stuns, it was still a reasonably fair encounter with one exception, the fall. As a DM, you have to be really, really careful about any terrain piece that can kill a player outright, which that fall could. I think that was your only real mistake in design and it wasn't that terrible. It's a cool idea, but at your player's level, a forty or fifty foot tower is a little fairer, not nearly as deadly, and still invokes the same level of tactical thinking.
From what you've posted it appears that you and your players might still be kind of getting the hang of a few aspects of 4E. That's fine, that's one of my favorite parts of the new system. But sometime miscalculations might happen. In that case, consider either fudging a little (e.g. adjust the falling damage to that PC didn't outright die the second time), or perhaps even better, give your players a bit of a reset button to help them out. When my group was just learning the game, I gave them 5 miracle man chocolates which could raise the dead instantly. It gave the group a safety net for all the mistakes we made while new to the system, and kept the story moving along when those mistakes did happen.
Talk with your player, tell her it wasn't personal, and just let her know that sometimes that stuff happens in D&D. Next time it will be someone else. Hopefully your players are willing to suck up the occasional bad night or forgive you & the dice for unexpectedly difficult encounters. The fact that your group takes the time to sit down and talk about how to make the next gaming session go better, tells me this is probably true and that in the long run you guys will do just fine.