UPDATE: Since writing this post in August 2017, several important changes have taken place in the laws regarding ADA compliance for websites. On December 26, 2017, the Department of Justice announced that they have withdrawn the Obama-era Advance Notice of Proposed Rulemaking mentioned in this article which intended to require ADA website compliance. The DOJ’s withdrawal announcement stated, “The Department will continue to assess whether specific technical standards are necessary and appropriate to assist covered entities with complying with the ADA.”
I should mention one caveat to all of this. Businesses that are required to comply but don't have the ability to bring their websites into compliance can provide an accessible alternative to provide the same information, goods, and services that they provide online, like a staffed phone line. The trick, however, is that this option has to provide at least equal access, including in terms of hours of operation. And, as we know, the internet is around 24/7, so good luck with that.
Once you have been hired and started work, your employer cannot require that you take a medical examination or ask questions about your disability unless they are related to your job and necessary for the conduct of your employer's business. Your employer may conduct voluntary medical examinations that are part of an employee health program, and may provide medical information required by State workers' compensation laws to the agencies that administer such laws.