Thanks for writing. While I’m not a lawyer I believe if your physical practice is ADA exempt your web presence, as an extension of that physical business would maintain the same exemption status. If you’d like to be absolutely certain I’d confer with an ADA lawyer (email us, questions at yokoco dot com if you need a referral) but I don’t believe you have reason to worry.
If you are applying for a job, an employer cannot ask you if you are disabled or ask about the nature or severity of your disability. An employer can ask if you can perform the duties of the job with or without reasonable accommodation. An employer can also ask you to describe or to demonstrate how, with or without reasonable accommodation, you will perform the duties of the job.
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. 
However, in states that have enacted laws that allow private individuals to win monetary awards from non-compliant businesses (as of 2008, these include California, Florida, Hawaii, and Illinois), "professional plaintiffs" are typically found. At least one of these plaintiffs in California has been barred by courts from filing lawsuits unless he receives prior court permission.[55] Through the end of fiscal year 1998, 86% of the 106,988 ADA charges filed with and resolved by the Equal Employment Opportunity Commission, were either dropped or investigated and dismissed by EEOC but not without imposing opportunity costs and legal fees on employers.[50]

The average cost for hiring a web designer varies greatly depending on the scope of the work, which may range from building a site from scratch to rebranding an existing one, as well as the amount of content and graphics the designer will create. In general, the more complex the project, the more time the design agency will have to spend. Because web designers often work on an hourly basis, the longer the project, the higher the costs; you can count on the web designer spending at minimum 10 hours to create a very basic website with just a handful of pages with few elements. Prices also depend on the designer’s skill set, the process, and the company’s rates. In general, the national average cost for a basic website package starts at $500, but a customized website can cost as much as $2,000 or more. Here are typical average hourly rates, broken out by the complexity of the work:
I am from Texas and I own my own business, DanzerPress LLC, where I work as a freelance WordPress Engineer part-time. I previously worked for Multiply/Answers.com as a Full-Time Software Engineer. My skills in Front-end Languages include: HTML, CSS, CSS3, Responsive Design, JavaScript, jQuery, SASS. My Back-end Languages include: PHP, MySQL, and PHPmyAdmin. Build tools/Engines I use: gulp, webpack, npm, Timber/Twig....
I know there may have been concerns that the ADA may be too vague or too costly, or may lead endlessly to litigation. But I want to reassure you right now that my administration and the United States Congress have carefully crafted this Act. We've all been determined to ensure that it gives flexibility, particularly in terms of the timetable of implementation; and we've been committed to containing the costs that may be incurred.... Let the shameful wall of exclusion finally come tumbling down.[41]
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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