"I am lying beside the window."
Translation:Az ablak mellett fekszem.
Ok, so this one rather annoyed me. It seems to me that many of the sentences in this section could be translated using the -nál/nél construction, or with another construction such as mellett. Indeed, I think that "by" translates better with mellett, although in reverse it's true that "-nál" sometimes translates best as "by".
Why doesn't this one accept "mellett" or "-nál"?
It should be accepted. There is some difference between "-nál" and "mellett", especially in some other situations, but English is more liberal here. So, both solutions should be reported, and accepted.
fekszik is an -ik verb; those have -m in the indefinite conjugation for én (which looks like the normal definite ending, yes).
No, for the same reason that "I am lying the window beside" does not work in English.
"beside" is a PREposition, which means that it stands BEFORE its noun: "beside the window" (first "beside", then "the window").
mellett is a POSTposition, which means that it stands AFTER its noun: az ablak mellett (first az ablak, then mellett).
English has one common postposition: "ago". We say "I moved here three years ago." But we can't say "I moved here ago three years" -- that's like saying mellett az ablak.