Translation:The cat is lying in front of the television set.
It says the correct translation is "the cat is laying before the television" but in English we would almost never say this. Only perhaps in poetic speech or some other outdated mode of language. While "przed" may technically mean "before" also, in most contexts (or at least a simple one like this) I think certainly we would always say "in front of". (I am aware Duolingo accepts this, I'm merely clarifying the usage)
That's incorrect. "Laying" is not old fashioned. "To lay [down]" is an active verb. You lay something, an object, usually down. For example, "I'm laying the television down while I connect the brackets to it."
"Lying," "to lie" is a passive verb. "The cat lies/is lying in front of the television."
Where it gets confusing is that the past tense of "lying/to lie" is "lay." "Yesterday, the cat lay in front of the TV all day." But the past tense of "to lay [down]" is "laid." "Yesterday, I laid down the TV on its back."