Learn English – the difference between “analysed” and “analyzed”

In front of is a common phrase which functions as a compound preposition: in modern English it has almost completely replaced before in a spatial sense. If you try to analyse it, you need to interpret "the front of" as referring to a space outside the thing, which is a relatively uncommon meaning for it.

In the front of is not an established phrase in English, and so would normally be interpreted literally: "inside the front part of something". It is not common, because "the front of" something is usually a surface, and we don't often talk about things being in surfaces. An example where it might occur is I've got some water in the front of my watch, where we could understand "the front of my watch" meaning the space between the glass and the watch face.

In many contexts, the meanings are pretty much the same, but you might hear finished more often than completed in casual conversation. For example:

I've finished my shopping.
She finished the song.
He finished the race.

I could use completed in those sentences – the meaning wouldn't change, but the register might sound off.

The word completed can convey some sense of accomplishment. In the context of a race, it might work when the race is a major achievement:

He completed his first marathon last year.

Homework, though, is not really a major achievement, so I think you'd hear finished more often in casual conversation:

“Joey, where are you going? Did you finish your homework?”

That said, you might see completed in more formal contexts, such as a paper on education, or a course syllabus:

Students must complete six homework assignments during the semester.