When asbestos fibers become airborne, they enter a person's respiratory system. These fibers scar and damage the lungs and often lead to serious cancers like mesothelioma. Like many dangers in the house, asbestos isn’t easy to see when it could be causing serious damage. The amount of time exposed, combined with the person’s tolerance for asbestos inhalation and the amount inhaled, will all contribute to health problems.

No, but it’s common that they do. Gravity furnaces weren’t terribly efficient so wrapping either the ductwork in asbestos, the furnace itself, or both, was something done regularly. This allowed the system to retain more heat. At the time, this greatly enhanced the efficiency of the furnaces but it wasn’t until later that we became aware of just how carcinogenic and dangerous asbestos could be.

No, you do not have to worry about new popcorn ceilings having asbestos. All residential building materials used since the mid-1980s stopped including asbestos, so new popcorn ceilings have no risk of asbestos. You can still create a textured drywall ceiling with a popcorn texture if you like, but new techniques have no risk of adding asbestos. 

Bathroom tiles can contain asbestos, just the same as patio tiles or kitchen tiles. Remember that asbestos was used primarily for its insulative and fire-resistant properties, both of which are desired in a house. Before we knew asbestos caused cancers and other diseases, it made a lot of sense to include it in many different building materials, including bathroom tiles.