For small water purification look into the STERIPEN.

For the first aid kit, I would recommend some benzalkonium chloride towelettes. They are a disinfectant that can be used directly in a wound without damaging tissue.

REI Waterproof matches are great. I am a fan of Swedish fire steel.

A small knife does work just fine, but I love my Kabar.

You may want to consider carrying a small ziploc bag with some sort of an electrolyte replacement in it. Just make sure you try it before hand to see if you like it.

You didn't mention what you were going to start out wearing when you are hiking. You will want to be sure to bring some good layering clothing. If the weather turns on you, and you can't get a fire started you need some way to stay warm enough through the night.