A. No. The ADA requires that the employer provide the accommodation unless to do so would impose an undue hardship on the operation of the employer's business. If the cost of providing the needed accommodation would be an undue hardship, the employee must be given the choice of providing the accommodation or paying for the portion of the accommodation that causes the undue hardship.
The type of operating system and hosting doesn’t matter much for design, but the platform is a factor. For instance, if you need a WordPress theme, the designer must work with WordPress themes and customize them in a way that a developer can feasibly code in CSS or JavaScript on the front end. If you use another CMS, the developer must work with those elements. Most designers specialize in specific platforms, so review their portfolios and experience for specific platforms before you invite them to bid on your project.
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.  

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.

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