Sessel also means chair?
How can one distinguish between "dich" and "euch"?
In this case, you can't.
One could argue that you normally offer one chair to one person (e.g. at a table), but this could also be about giving a chair to a couple for their household, so "für euch" works as well.
Why isn't it Der stuhl ist fur du
For the same reason that "The chair is for he" or "The chair is for I" would be wrong -- you need an object form, not a subject form. Thus dich and not du.
Der Stuhl ist für Sie/dich. The first accepted.