Kurt, most of those deaths were because your bed was right in the area the mobs were at. I don't think challenge mode is too hard, you just have to be smart.
Tip: When caving, take a flint&steel and some netherrack with you so you can light stuff.
Also block off any caves you're NOT inside with cobble or something, so creepy crawlies won't sneak up behind you.
And when you die, don't run back in willy nilly with nothing, you won't get anywhere without a sword and a little bit of armour to press forward.
oh yeah and make sure you have somewhere to run to BEFORE you light TNT
Hope this helps.