I've always heard "teshuvah" in religious settings meaning "repentance" or "return." Is this the same as תשובה here?
Yes, absolutely. The commonly used term teshuva=repentance is a mistranslation. It comes from returning to the proper path, and a common way to achieve this is to repent. (A better word for repentance is חרטה charatah.)
Why do I hear "ch" sound in the word "answer"? Is this a special combination of letters or something? I thought it would be something like hatashova or hatashuva
The English sound "ch" is actually just "t" followed closely by "sh" (focus on where your tongue is when you slowly say "change", for example). For this reason, tshuva can sound like chuva to an English speaker.
What about ?איזו התשובה שלנו? Is this acceptable in Hebrew? In my language we literally say "Which is our answer?", as "What is our answer?" wouldn't make any sense in most contexts.