Short answers, pulled from the story.
Chimneys were invented in northern Europe in the 11th or 12th century. They solved the problem of smoke more reliably than earlier methods, allowed fireplaces to have a draft, and made it practical to install multiple fireplaces in a single building.
Count Rumford designed a fireplace with a tall, shallow firebox that was better at drawing smoke upward and out of a building. The shallow design also greatly improved the amount of heat radiated into the room.
A literature review in the Journal of Toxicology and Environmental Health linked prolonged wood smoke inhalation to chronic bronchitis, interstitial lung disease, and pulmonary arterial hypertension in adults. Children face the greatest risk, including decreased lung function, increased acute bronchitis, and higher rates of respiratory infections. Wood smoke contains potentially carcinogenic compounds including polycyclic aromatic hydrocarbons, benzene, formaldehyde, and dioxins.
Standard modern wood-burning masonry fireplaces are required to achieve at least 80% efficiency; Salzburg, Austria, is cited as one jurisdiction where this is the legal minimum. Older fireplaces typically have much lower efficiency ratings.
John Adam, Robert Adam, and James Adam were the most renowned fireplace designers of the Industrial Revolution era. They perfected a style that was smaller and more brightly lit, emphasizing the quality of construction materials rather than size, and their approach was used for generations.
Ventless fireplaces, also called duct-free or room-venting fireplaces, are fueled by gel, liquid propane, bottled gas, or natural gas and do not vent exhaust to the exterior. They must be properly sized to the area being heated, and an oxygen sensor and a carbon monoxide detector are safety essentials because they release moisture and combustion byproducts directly into the room air.