Cześć! Ja uczam się Ja uczę się (You can drop the subject "ja") polskiego i mam pytanie:

Dziękuję wszyscy wszystkim!

What is the correct case here?

Mieszkam w nowym domu.

"W" in this case I thought was locative, -> That's right, it's locative case. It answers the questions where? about what? and about whom? The answer is always noun with preposition. For example:
- where?: In the house. = W domu.
- where?: On the road. = Na drodze.
- where?: Next to the house. = Obok domu/ Przy domu.
- about whom? = About you. = O Tobie.
You shouldn't concentrate on the ending. Rather try to focus on the question.

Greetings!

Update: "Mieszkam w nowym domie?" - It's incorrect.

the nouns like DOM, SYN, PAN are really tricky. You are right that if you follow rules of Polish grammat nouns ended with -n and -m should have -ie case ending. But... (in Polish grammar the "but" is even more important than rules you have to learn) mentioned nouns for historical reasons demand in locative -u ending (old slavic grammat!!!) 

But... but ... but ... is you deal with new words where for example the word DOM is part of, then when you inclect in locative the endings gonna be -ie for examples artdom - w artdomie! 

as regards the preposition this site would be helpfull for you. 

https://en.wikibooks.org/wiki/Polish/Prepositions_as_hints_to_declensions

Cześć!

I just want to add one more thing: "Mieszkam w domu" is a locative case. It can be confusing, because genitive case for word "dom" is also "domu". Here is how word "dom" would appear in different cases (I am skipping vocative):

Nominative: dom (example: It is a house, To jest dom)

Genitive: domu (example: I don't have a house, Nie mam domu)

Dative: domowi (example: Thanks to the house I have a place to sleep, Dzięki domowi mam gdzie spać - the example is complicated, because house is not a typical target for the dative case)

Accusative: dom (example: I see a house, Widzę dom)

Instrumental: domem (example: I am going to share my house with him - Podzielę się z nim domem - again, not a typical target for instrumental case)

Locative: domu (example: I live in a new house - Mieszkam w nowym domu)

The -ie ending for masculine nouns in locative case is not a rule, it depends on the word and its ending. For example:

  I live in a house - Mieszkam w domu  (masculine word: dom)

  I live in a garage - Mieszkam w garażu (masculine word: garaż)

  I am lying on a blanket - Leżę na kocu (masculine word: koc)

  I am walking on snow - Idę po śniegu (masculine word: śnieg)

Good luck with your learning!