"What if you gave them more time?"
Translation:Et si tu leur donnais plus de temps ?
I think because "more time" is the direct object. not them. So, "Je les aime", but "Je leur donne un chat"
"et si ?" is the idiomatic French equivalent of the English "what if ?".
It doesn't correspond to it litteraly, but it has the same meaning.
No. They are teaching something new. That doesn't mean the old thing is wrong. Focus on the new thing now, but remember the old.
You have three mistakes in your sentence:
si + hypothetical clause calls for the imperfect (like in English: "what if you had..." as opposed to "of what if you give..."):
Et si tu avais donné...
object pronouns are always placed before the conjugated verb (the auxiliary verb in this case), except in the imperative:
Et si tu leur avais...
leur is not the direct object, but the indirect object (the direct object is "plus de temps"), so donné does not agree with it:
Et si tu leur avais donné plus de temps ?
Also, this sentence means "What if you had given them more time?" which means you cannot give them more time anymore, but you're wondering what happened if you had.
But I think English allows to use 'if you gave' instead of 'if you had given', so maybe it can be accepted.