Make sure you've weathered your costume if you're going through the trouble of weathering yourself !
Is there a specific reason you want a toothpaste tube ? I'd probably use a paintbrush, sponge, towel, fingers, pressing to transfer, whatever to do the blood on the clothing - and for the body I'd probably be using a makeup brush or sponge and even fingers to apply it from a palette or cakes of makeup with perhaps some of the "fake blood" stuff for the stuff that's supposed to look fresher - you can apply excess to the wound site and then move around a bit to get a natural sort of transfer, too. There are even recipes online for making fake blood. Ben Nye and likely others sell "bruise" and "wound" palettes that are the colours you'd want bundled together.
For the dirt/soot you'd just want a powder makeup in that colour and possibly other stuff like a black cake makeup + a stipple sponge or even liquid eyeliner. Even mixing a bit of powder in water and staining yourself that way, or wet sponge plus cream cake.
This is the kind of thing that you play around with and have to practice a bit - I think the skill is most like being able to paint - knowing what variations of dark and light you want to achieve. You'll get much better control when applying with a brush as opposed to trying to squirt it on like cake frosting.
I would recommend you try to find a theatre or dance supply store locally that carries this kind of makeup and going in - they'll be able to get you what you need and give you advice and can even show you how to use the products. The place near me is a "dance" store but they carry a large range of all products and can order what they don't have in stock - and the senior worker there also teaches stage makeup classes at the local college.