Answer: The federal Fair Labor Standards Act (FSLA) provides guidance on what constitutes a job that is exempt from overtime. To be classified as an exempt employee, the position must meet three tests: Be paid at least $455 per week; has a "guaranteed minimum" amount of money s/he can count on receiving for any workweek in which s/he performs "any" work; and whose job duties are either executive, administrative or professional. Here is a link to a more detailed explanation: http://www.flsa.com/coverage.html

Answer: The Act prohibits employers from discriminating against qualified individuals with disabilities in job application procedures, hiring, firing, advancement, compensation, job training, and other terms, conditions, and privileges of employment.

If an organization has 14 or fewer employees, it is exempt from the Act. In addition, an employer generally does not have to provide a reasonable accommodation unless an individual with a disability has asked for one. For more information see:
https://www.eeoc.gov/eeoc/publications/fs-ada.cfm

Answer:  The size of the organization and the extent to which the organization receives federal funds (such as grants) will impact the requirements.  A usable online tool provided by the US Department of Labor will guide you through determining your requirements: https://webapps.dol.gov/elaws/posters.htm

New Mexico poster requirements may be found at: https://www.dws.state.nm.us/Business/Publications/State-and-Federal-Posters

Answer: Yes. For example, in a childcare facility doing playground duty, the ability -or lack of- to move quickly (mobile), may impact child safety. Similarly, hearing and the ability to respond to sounds such as distress calls is often an essential job ability.
When working out of doors the jobholder may be exposed to extreme temperatures. Identifying these physical requirements also impacts making reasonable accommodations for disabled (or temporarily disabled) employees.

Answer:  Yes, with limits. New Mexico Stat. 1-12-42 states:  
A.   On Election Day a voter may absent himself from employment in which he is engaged for two hours for the purpose of voting between the time of opening and the time of closing the polls. The voter shall not be liable to any penalty for such absence; however, the employer may specify the hours during this period in which the voter may be absent.    
B.   The provisions of Subsection A of this section do not apply to an employee whose work day begins more than two hours subsequent to the time of opening the polls, or ends more than three hours prior to the time of closing the polls.    
C.   The provisions of Subsection A of this section apply to elections of Indian nations, tribes or pueblos for a voter who is enrolled as a member of the Indian nation, tribe or pueblo and is qualified to vote in the election.