Try melt the grease/tallow and soak napkins/toilet paper/any soft paper in it, let it cool. I call these things "fireslugs" and they are perfect for lighitng fires in rain.
Of course, I have many more ideas, but they are too evil to post them there

.
EDIT: It is easier to post them there than to PM two people. You all are just sooo lucky I cannot believe it

.
Okay: Waxes, grease, tallow and butter can be used to make a violently burning mixture by melting them and letting sawdust, napkins, toilet paper, shredded straw, thin wooden shavings and such absorb it, then letting it cool. Wax and sawdust is best of all wax mixes and shoe polish with a napkins is good too, shoe polish alone burns well and if you add sawdust to it, sticky, very flammable paste is the result. Tallow and grease are generally better for use with absorbent paper than anything else and they are runny when they burn, igniting anything they are lying on. Pitch is good to add in bigger pieces to paste or jelly-like mixtures to prolong flame duration. Also, napalm with several golfball-sized pieces of wax-sawdust mix is interesting... They burn and roll away, spreading the diameter of destruction. My most dangerou invention is called "Inferno in a jar" and is composed of styrofoam napalm to which sulphur-KMnO4 mix is added. This mix is unstable, so mix shortly before use. Mix well and light. It cannot be extinguished by normal means and the temperature is extremely high, enough to warp metal things in proximity and burn through thin sheet metal.
Also, lighting pool of napalm in which a butane pressure bottle for blowtorch is floating yields interesting effect, as well as placing small charge of black powder under a bag of gasoline... but that's no longer primitive, I see.
Quick and dirty way to primitive incendiary: Melt anything waxy or gresy, soak it into something flammable and porous, ideally divided into fine particles, and you have fine incendiary.
Easiest explosive(propellant) is made by dry mixing saltpeter and sugar. Wet mixing(add hot water until it is dissolved, then cook it on low heat until it has fudge-like consistency, then spread it on a sheet, dry a bit and press through a window mesh to granulate, dry further) is better, after that you have something that can power a shotgun or some other long-barreled big bore. It burns too slow to be of any use for pistols. Bottle-necked rifle cartridges are good and long barrels are mandatory, but the power is good.
You can make ceramic grenades from this propellant and thick-walled round shaped clay vase. Power is not great, but then again, what do you expect from thing that is around from the invention of means of obtaining saltpeter from manure?
DISCLAIMER: I am not responsible for anything you do with this information or any information for that matter. If you blow something up or burn it down, you are on your own. Enjoy.