"How are you feeling today?"
Translation:Як ви почуваєтеся сьогодні?
It's correct, but please bear in mind that all the sentences in the course were added by hand, and sometimes the team members just overlooked some absolutely correct variants.
Unfortunately, the team is not very active recently, so it's unlikely that these things will get fixed soon.
It is reflexive ending. Just like "I am teaching myself" - я навчаюСЯ, "you may cut yourself" - ти можеш порізатиСЯ. -ся is the short version of the reflexive pronoun себе. Like Polish się, German sich, French se.