"I am here because my place is here."
Translation:Я здесь, потому что здесь моё место.
No, we don't, because it depends on the meaning. We use "потому что" when we translate "because", and we use "потому" when we translate "so", "thus" of "therefore". The first is about the reason (I am here BECAUSE my place is here), the second is about the result (and the sentence might be like this: "My place is here SO I'm here", "Мое место здесь, потому я здесь").
За то что (spelt separately!) is literally "for that [fact], that..." and as such is a very restrictive sort of "because". E.g., Я ненавижу тебя за то, что ты предал меня = I hate you because you have betrayed me = I hate you for the fact that you have betrayed me. It basically works with the verbs that would allow "for [something]" in English: you can hate/love/thank for something, and in Russian you would be able to use "за то, что" to expand that statement.