Here are my questions...
1. Anyone have the LEE moulds, and how well do they work?
They work very well. Follow the directions and smoke them first, and they'll work great.
2. Are there common around the house type things to use for a smelting pot, and dipper? (Yes, I'm trying to be cheap.)
Look for a small cast-iron pot at thrift stores, although that sort of things has become harder to find because people have awakened to its excellence for cooking, and also use it for decorating. Do NOT use cast aluminum! Aluminum will soften over the heat source, and the lead will punch through the weakness and spray molten lead all over.
Similarly, never allow any kind of water (sweat, rain, sprinkler, drink, etc.) anywhere near the open pot of molten lead. A drop of water hits the molten lead, goes just under the surface, turns to steam, and blows molten lead all over. Trust me, you don't want the heat of the molten lead traveling up the strainer's shaft and melting your plastic handle. I hear tell a certain ol' desert cat once did that.
Asian grocery stores are good places to find large, slotted spoons with wooden handles. Make sure the spoon is stout and at least 14 inches long.
For a dipper, purchase a cheap metal vegetable strainer. Buy one with a wooden handle, or remove the plastic handle and replace it with a wooden handle or tree limb. Make sure it's securely affixed; use two bolts.
3. I plan to just have a small campfire for melting the lead. Does this work in real life, or only in the movies?
That's movie stuff, based on fact, but take it from one who has tried casting from campfires: roasted knuckles smell like burning hair! Even with gloves, you hands will get too hot. It's a real pain to cast bullets in a fire. Use a stout propane stove. It needs to be stout to support the weight of the cast iron pot and its lead. I used a camp stove a few years ago. The stove's grill got red hot over the flame (duh), weakened and sagged down from the weight of the pot and lead. Scratch one stove.
4. What about flux, and release agent for the mould?
Bullet lburicant, tallow or even candle wax work as flux.
Mould release is not needed with Lee moulds, if you smoke them as directed.
5. Sources of lead?
I have a small shooting range at my house, and I was thinking about mining the backstop to get the lead out of it. There would be other types of bullets mixed in with the cap and ball lead. Shotgun slugs, .308 win., buckshot, and lots of.22LR. Plus whatever the previous owner left in it.
Shotgun slugs are nearly pure lead. So are .22 bullets. Either will be good. Buckshot is typically hardened with antimony. If you can dent it with your fingernail, however, it will be fine. The core of most jacketed bullets is pure lead, to aid expansion. Or, it's so close to pure that It may be considered as such.
6. How do you know that the lead is soft enough?
If you can dent it with your fingernail, it's soft enough.
7. How do you get antimony,zinc, or other alloys out of the lead so it is soft enough?
There is no way to remove the other ingredients/elments from lead once it is alloyed. At least, that is my understanding. Perhaps some will rise to the surface, to allow skimming, but I suspect most of it would remain in suspension. But go ahead and cast a dozen balls with what you have, and try it. You may find that you're worrying about nothing.