Learn Swedish: Vi tvingar dem att korrigera sina fel. - We force them to correct their own mistakes.

This sentence features an object-controlled reflexive. The grammatical subject is vi (we), but the object dem (them) is the one actually performing the action of correcting. We call dem the "logical subject" of the infinitive verb att korrigera. Because they are correcting their own mistakes, we use the reflexive sina to refer back to this logical subject.

What would happen to the meaning if we used deras instead of sina?

The meaning would completely change. If you wrote Vi tvingar dem att korrigera deras fel, the word deras (their) would refer to a third, separate group of people. It would mean we are forcing them to correct someone else's mistakes, not their own.

Since fel is an ett-word, why do we use sina instead of sitt?

Fel is an ett-word that looks exactly the same in its plural form (ett fel, multiple fel). The use of sina tells us that the word is plural here, meaning they are correcting multiple mistakes. If they were only correcting one single mistake, you would use the singular ett-word form, sitt fel.

Is the infinitive marker att strictly required after ?