Toiletpaper = good water filter for mud and other particles.. so yes moar toiletpaper.
Good idea, actually, never thought about that. Standard coffee filters work, too. Of course boiling water should also be done, because that´s the easiest way to kill bacteria and germs.
On another subject:
A medical bag is also really important. There´s no need for high-tech surgical tools, but standard stuff, like bandages, dressings, gauze (can be used to start a fire btw), a bandana or a similiar scarf and of course basic medicaments, like prescription free pain killers or anti-diarrhea pills are important, too, especially the latter.
If you need special drugs for whatever medical reasons, make sure to have those, too. And always read the package inserts. You don´t want to give someone with a heavily bleeding wound painkillers that thin blood (such as aspirin)...
Another good idea would be a so-called readily packed "bug out bag" which contains the bare essentials for three days, such as water, food, spare clothes, medical supplies, a tarp, maybe a sleeping bag etc.
So if you have to quickly leave your "hideout" you can quickly retreat, without having to pack all your essential gear. Just google "bug out bag", there are tons of "prepper" or survivalist homepages that deal with what you should have in your BOB.
This thread is actually quite cool. Maybe we can use it as some sort of "outdoor and survival"-thread instead of a "what kind of apocalypse will end our civilisation".thread? ^^