Your site would need to have a text only option, with all functionality accessible through a keyboard for visitors with mobility issues. Once you make these and other changes to meet ADA guidelines, your site would need to be tested by a website development company familiar with ADA compliance issues to be sure that visitors who use assistive technology such as screen readers are able to access your web content fully.
The ADA statute identifies who is a person with a disability, who has obligations under the ADA, general non-discrimination requirements and other basic obligations. It delegates fleshing out those obligations to federal agencies. The agencies issue regulations and design standards. The regulations have the details on the rights of people with disabilities and responsibilities of employers, state and local governments, transportation providers, businesses and non-profit organizations. The design standards specify how many entrances need to be accessible, how many toilet rooms and the design for those elements.  To know what the ADA requires, you need to read the law, regulations and design standards.  
You are correct, ADA defines an “employer” as any person who is 1) engaged in an industry affecting commerce; 2) employes 15 or more full-time employees each work day; and 3) for at least 20 or more calendar weeks in the year. In the context of physical spaces, ADA would not apply to companies with fewer than 15 employees. However, courts don’t seem to have come to a consensus on what digital compliance really should look like. Because websites can be accessed anywhere in the country, small business owners might potentially face lawsuits in unfavorable jurisdictions. If you are a small business owner, I would recommend consulting with an accessibility lawyer and ask what they recommend.
The words in the tag should be more than a description. They should provide a text equivalent of the image. In other words, the tag should include the same meaningful information that other users obtain by looking at the image. In the example of the mayor’s picture, adding an “alt” tag with the words “Photograph of Mayor Jane Smith” provides a meaningful description.

Most recently, however, pizza chain Domino's has been brought under suit for their website not being accessible for specialty ordering. The U.S. Supreme Court refused to review the case, instead upholding the decision of the 9th U.S. Circuit Court of Appeals who said the “alleged inaccessibility of Domino’s website and app impedes access to the goods and services of its physical pizza franchises—which are places of public accommodation.”
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