Very broadly speaking, E&O coverage should cover the examples you cite, including bad advice:

Professional
liability insurance protects against allegations
of a “wrongful act” defined by most policies
as “An act, error, omission, misstatement, misleading
statement or neglect or breach of duty”. Policies
specifically don’t cover bodily injury, property
damage, and claims arising out of the use of a car,
boat or plane. Also excluded are claims resulting
from an employment injury or employment practice.
All such events are covered by other policies—general
liability, auto liability and workers’ compensation
insurance, for example. Professional liability insurance
protects a consultant from allegations that the job
was not done right or that the job was not done well
enough.

However, like all insurance policies, terms of coverage will vary, so don’t assume - shop around and make sure you know exactly what a particular carrier will or will not cover.