No doubt this varies geographically, but I hear 'thank God!' used as an interjection all the time, and 'praise God!' almost never (other than in the literal invocation to do so in a religious context). Both of these should be acceptable translations if the Arabic phrase amounts to much the same thing.
Here I definitely agree, although it does depend on context. While in this case 'thank God' is probably the closest natural translation into English, I'd argue that's because we really only use that expression to express relief at avoiding something bad (i.e. potentially losing your phone), or to express great happiness at something achieved. In Arabic, the expression is used both in those contexts, and to express one's enduring 'background' thanks to God for any good action/result/state. What this implies is that the الحمد لله used when answering the question 'How are you?' should idiomatically be translated differently to the one used here. In the case of the former, I'd say 'thanks be to God / praise God' is normally most suitable, and 'thank God' is more appropriate for this telephone example.
I'd like some help understanding "there" in Arabic, since "there" can mean different things in different languages. Is this an appropriate thing to say to someone after calling your friend whose house you just left (where you now know you left your phone)? Can you also say it pointing across the room at your phone? What other contexts are appropriate or not appropriate when using هنك?
Actually you may pick up these as you go, as Arabic is a very vast language. Even Duolingo doesn't cover many aspects of it. But in the cases you mentioned, yes هناك is appropriate. It is used as a place in sentences. "I left my phone there" or "let's go there". But it is also used to denote the absence or presence of objects. "My phone is there". Hope this cleared it up for you a little bit :)