Iron sediments from rusty pipes are not likely to cause health problems. While a glass of yellow-hued water is off-putting, it is generally safe to drink yellow water in the short term. But you certainly want to address this problem. In the meantime, switching to bottled water until the yellow water issue is resolved is a good idea. 

No. Standard homeowners insurance does not cover any kind of lead remediation, focusing instead on sudden, unpreventable events like fires and theft. Many insurance companies will specifically exclude lead paint removal, since it tends to be an expensive and unavoidable project. The exception is if the lead surface is damaged during a covered event (like a flood) and homeowners insurance pays its replacement.

Mold, VOCs, radon, carbon monoxide, and particulate matter are typically measured.

Lead toxicity comes from inhaling lead or consuming it. Before the 1980s, when the government banned lead from consumer use, it could be found in paint, plumbing, pipes, ceramics, and even gasoline. Lead paint is toxic for the same reason lead itself is toxic, which is why lead poisoning from paint presents the same as lead poisoning from water or food sources, with a slight increase in respiratory symptoms vs. digestive symptoms. Lead paint is most dangerous when it’s old and peeling, cracking, or otherwise disturbed. This increases the concentration in the air and, therefore, in breathable air.