"In the front" locates you inside whatever is being discussed. My understanding of "z przodu" is that it locates you not inside, but "in front".
z przodu can be for example in the front of the car or the line or the train
przed means in front of sth
Being "in the back of" or "in back of" is an Americanism when used like this. In England you would have to say "behind"
Currently, yes, but you might be surprised to know it has its origins in the UK and is merely a turn-of-phrase that died out over there. There are all kinds of features of American English, especially in the south, that have more in common with early modern English than the UK's modern English does.
It's referring to front and back in, say, a train, as in front or back row.
It doesn't have to switch between "at" and "in" for front vs. back. Both work:
In the front/in the back
At the front/at the back
I would balance the sample as 'at the front' and 'at the back' to avoid the inevitable wondering why the difference.
"Out front" should be accepted - "in front" is much more specific and uncommon, whereas "out front" means precisely this (in relation to location).
If you use the slow audio (or hover over one word), the one-letter prepositions will be read the way they're read when reciting the alphabet.