Buy a thermometer for measuring molten lead temperatures. It will help you control the heat on an open fire.
Look around the flea markets for an electric grill use for pop corn popping. They are cheap enough even for college students to have one. They produce enough heat to melt lead. If you have a big grill, and small pot, it might help to use some scrap sheet metal to make a reducing flange or collar, to fit the grill, and funnel the heat to the pot. The flange will also keep you from burning your hands as you dip the lead out of it.
If you are melting lead out doors, just make sure the wind is not blowing into your face. If you are choking on the smoke, the wind is blowing into your face. ERGO, MOVE!
As to lead poisoning in adults, one of my good friends was a firearms training instructor at a local Police academy, when they were shooting in a closed, unventilated area. The College tested all the range officers and staff for lead levels, back in the 1970s, and found all had elevated levels. This lead to some renovations to the range, including ventilation and filtration systems for the vents.
He was tested thereafter annually, after being transferred to class room teaching duties, and they found his lead levels ( in his blood) dropped, and continued to drop over the next 2 years until they were well within normal levels. He completed his PhD. while all this getting rid of lead was going on, so I don't think the lead adversely affected him in anyway.
I don't know what the threshhold levels of lead in the blood are for adults, and I don't think the scientists have reached any conclusion for adults to date. The levels you see published for blood levels, by the Center for Disease Control( CDC) are for Infants, not adults.
You might point that out to your mother, too. If she remains concerned, your doctor can have your blood lead levels checked for you. He can also give you the most up-to-date information from medical research on threshhold levels for blood lead levels in adults.
In adults, lead is one of the heavy metals that your kidneys are designed to filter out, and remove from your body in your colon, along with aluminum, copper, zinc, iron, etc.
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The problem with lead poisoning has to do with infants, who are less than 4 years old. Their brains are still developing in those early years, and the fatty tissues absorb and continue to hold lead in low amounts if they INGEST lead paint, or acquire it, almost always orally, from some other source. This retention of lead occurs during those early years AS THE BRAIN IS DEVELOPING. When the brains stops growing, it stops absorbing and KEEPING lead in its tissues.
When I was older, as a child- probably 6 and older-- we used a piece of lead as our " marker" to play Hopscotch on the sidewalk. It proved to be far superior to any kind of rock, flat or not, that others used, because it stayed PUT when it landed. The lead blackened with oxides, and were handled constantly. I am sure that some traces amounts of lead got into our mouths, and blood system from all that handling, but none of us experienced any ill effects from the experience.
You might look up Lead Poisoning on the Internet, and find some articles on the subject that can ease your mother's mind. I am sure I could find articles about the question of lead poisoning from casting balls and bullets. Mankind has been doing this kind of work for Hundreds, if not thousands of years.
The only historic deaths I have read about that have been found caused by lead poisoning, were some mariners, who were marooned in pack Ice in the Arctic Ocean, who died of lead poisoning, because the tins of food they ate had been soldered with pure lead, both at the seams, and around the lids.
The bodies were discovered on an Island in the Arctic, and found to be in much the same condition as when they were buried. Scientists thawed out the bodies, after chipping them out of their graves, performed autopsies on them, including toxicology tests, which determined that lead poisoning was the Cause of Death. A search of the camp dump uncovered the antique cans that held the foods, and the lead oxides in the joints, and traces of food still frozen, that matched the lead found in the bodies.
Other than people exposed to high levels of lead dust, on closed shooting ranges, I just don't know of any other case of adults having high lead levels in their blood from other causes.
I am sure its possible if you breathe in lead fumes, but as BrownBear notes, Lead melts at about 620 degrees, and begins to fume at a temperature over 800 degrees. Simply using a thermometer to control the temperature of the lead in your pot should be a sufficient safety margin to protect you from lead.
There are cheap styrofoam masks you can buy at hardware, and paint stores, to protect you from fumes of all kinds, also.
Stand up wind, wear good protective gloves, shirts, pants, and SHOES, along with that mask, and then shower, and wash those clothes when you finish. Brush the shoes or boots to get lead dust off of them. The gloves can be washed, too, even if they are leather. Just use cold water, and soap, and rinse them well. If they dry too much, you can soften them with Neatsfoot oil.
If you then clean up the BBQ grill with soap and water and a steel brush, you should have no problems with Lead from your casting. In fact, there are more carcinogens in soft wood like pines, than you are going to find in either hard woods,or any charcoal you might burn in the BBQ pit. Don't burn painted lumber of any kind in your grill, as the paints can contain some nasty stuff, too.