The answer to your first question is a loud “Yes.” Employee engagement is all about motivating people to do that a little bit extra (“discretionary effort” as it is called) for the organization. To that extent, you would definitely want to know how engaged are the senior managers as well as other employees.
I agree with Shiju regarding Employee engagement survey being applicable to all levels. Your second question is slightly tricky. There can’t be a “ready template” study and you need to design a customized questionnaire that suits your organization’s unique business goals and work culture. Still, here is a set of guidelines. The survey should probe whether the employees (at every level):
Know what is expected of them in their job,
Have the skills and equipment needed to do well in their work,
Communication they receive is clear and personal in tone,
Receive recognition or praise for good work done,
Perceive the work environment as encouraging for development
Feel that their opinions and suggestions are counted,
Believe that their job role is important and aligned with company’s goals.
Participate in a one-to-one feedback discussion with their supervisor at least once in 6 months,
Have been sponsored for a learning and development program at least once in 12 months