This is a big topic, that requires a lot more research. Nevertheless, I have made some observations as a starting point.
It should of course be born in mind that medieval and Tudor people simply didn’t have the same ideas of hazard and risk that we do today, and that knowledge was not written down in manuals but something passed on through experience or verbally from the more skilled artisans.
Firstly though, all three jobs mentioned in the title are related in some way or another, and also to alchemy. Doctors see to sick miners, foundryworkers, alchemists and use substances produced by miners. Miners and alchemists deal with molten metals and thus would have been exposed to metal fume and carbon monoxide and anything else that was given off e.g. sulphur fumes.
Texts consulted include “On Divers Arts” by the 12th century Monk Theophilus, “De Re Metallica” by Georgious Agricola, “The Pirotechnia” by Biringuccio. The latter two are 16th century works.
So my searches for period mentions of hazards has found the following risks and attempts at reducing them.
Heat and sparks – you see aprons in illustrations in Biringuccio, Agricola and of medieval smiths and miners. This is one of the most basic protections, along with gloves.
Theophilus says not to suck when glassblowing at the wrong moment or the flame will come into your mouth.
Agricola writes, about smelting iron on an open fire, “In order that the heat of the fire should not burn his face, he covers it entirely with a cap, in which however there are holes through which he may see and breathe.”
Biringuccio wrote that you have to bake moulds well so that the bronze doesn’t splash out and the mould survives, so as to protect oneself from accidents.
Dangerous fumes and vapours:
Biringuccio reckons that a poisonous exhalation comes from arsenic, and that miners close their mouths and nose with a sponge wettened with vinegar. Orpiment and realgar are also dangerous. You should also avoid the smoke of brass whem melting it because it is a deadly poison that leaves men stunned, paralysed or stupid and gives them more diseases than he can name. This would be the zinc fume that rises from it as the zinc burns out of it. He certainly shows an awareness of the dangers of bad vcapours and metal fume.
Theophilus writes that you shouldn’t mill or apply gilding when hungry because the fumes of mercury (that’s the translation obviously, I don’t know what the original Latin says) are very dangerous on an empty stomach and give rise to sickness which can be treated with zedoary and bayberry, pepper, garlic and wine.
Agricola mentions pestilential air and the importance of good ventilation in mining shafts. The air is stagnant or rots the lungs. He also writes that when refining lead the foreman should eat butter so “… that the poison which the crucible exhales may not harm him, for this is a special remedy against that poison.” Oddly enough I have found a paper claiming that eating butter reduces people’s lead absorption by blocking the calcium channels in the gut through which it was absorved. Unfortunately I also found one that disagreed with that idea, so I am not yet sure if this remedy actually works.
Cellini (16th century goldsmith and bronze caster) wrote about gilding that “But none the less I saw that great masters aught not to practise this themselves, for he quicksilver that has to be used for it is a deadly poison, and so wears out the men that practise in it that they live but a few years.”
Relatedly, Cennini (15th century Italian artist) wrote that orpiment used as a pigment was dangerous to you, if you put it in your mouth from your paintbrushes.
Trip and physical hazards:
Theophilus mentions that workmen can get in each others ways when casting bells and removing stones from the mould furnace. You need agile workmen “… less someone’s carelessness should lead to a mould being bropken or one workman getting in the way of another or hurting him or provoking him to anger, contingencies which must be avoided at all cost.”
On the other hand, Cellini, when describing problems he had with inexperienced assistants during the making of a complex large statue, didn’t seem too bothered by such issues, but then he was well known for a cavalier attitude to danger.
So, what we can clearly see is that artisans and the people who doctored them knew about hazards and knew that what we call metal fume was in fact dangerous, and that mercury was poisonous. It is not always clear how they knew all this, but personal experience is important, as would surely be word of mouth. In the cases mentioned above, (and more in my notes) there is a concern with the dangers that you experience whilst doing your work, from the very materials you are using. In this way it is clear that they were not such ingoramuses as people might think.