Aloha Tatiana! I wish your questions had straightforward easy answers – and if you are government funded it kind of is. (See here: https://www.ada.gov/websites2_prnt.pdf) if you are not government funded, this is something that is currently being debated in the legal system. That being said, the WCAG 2.0 guidelines are a good set of guidelines to help protect yourself if you feel you should. (You can see more on WCAG here: https://www.yokoco.com/find-out-how-to-make-your-website-compliant/)
So, what do I mean by that? That sounds weird. So, when I say designer, I mean someone who's strictly an artist, and there's a lot of those out there. A lot of 'designers' are only concerned about the aesthetics of the site. What it looks like, or if its unique, or if it follows the latest website design trends. But at the end of the day they don't really 'get it' when it comes to what the primary purpose of a website is.