Translation:I am here because my place is here.
In the second use case, «потому́» can be replaced with a synonymous «поэ́тому», also an adverb. The former originates from the word «тот» ("that"), while the latter does from «э́тот» ("this").
With either word, «и» can be omitted.
Example: «Начался дождь, поэ́тому дети пошли домой».
It can be but is sort of bookish. The word means "for this reason". Поэтому is the word we normally use in this meaning:
- Здесь моё место, поэтому я (и) здесь. ~ My place is here, and that's why I am here.
- Я был занят, поэтому решил позвонить вечером. ~ I was busy so I decided to make a call in the evening.
- Сегодня будет дождь, поэтому я взял зонт. ~ It will rain today, that's why I have an umbrella ("took" it along).
- У неё мало денег, поэтому она не поедет с нами. ~ She does not have much money so she will not come with us.
You can, in principle, use потому in these sentences but it is going to sound odd. Потому-то somewhat less so.
Actually, most hits of потому without что in Russian National Corpus ended up being "потому как", which is an alternative of "потому что" (we sometimes use it in spoken speech).
Из-за is more like "due to" and only works with nouns. If you have a clause, you should use из-за того, что.
The preposition из-за, apart from its literal meaning ("from behind of"), is used to express the "culprit" of some negative outcome. That is, you consider some state unfortunate and say that the things are this way "because of" some fact, event, person or thing.
The audio is so fast (for a beginner who's been at this for months) that it might as well be gibberish. Trying to replicate what's being said on audio of this speed is useless and with almost complete certainty produces nothing a native speaker would understand as Russian.
Other on-line language programs do the same thing. It's counter-productive. One has to learn how to pronounce the words correctly first, before one starts to run words together and merge syllables/sounds at the ends of words with those at the beginning of the next word. This high-speed audio is just crap. Useless to a beginner. It makes no sense when you listen to it and makes no sense if you try to imitate it.