Learn Arabic (Modern Standard): ينام القط وراء الشجرة الكبيرة.

The word وراء means "behind." It is an adverb of place, and in Arabic, these act a lot like prepositions. This means it forces the noun directly after it, الشجرة (the tree), into the genitive case, which means it will end with a "kasrah" ("i" sound) if you are reading with full vowel endings.

Why does the sentence start with "sleeps" (ينام) instead of "the cat" (القط)?

This is the classic Arabic word order! While you can say "the cat sleeps" (القط ينام), it is much more common and traditional in Modern Standard Arabic to put the verb first. So, "sleeps the cat" (ينام القط) is the standard way to build this sentence.

Why does the adjective for "big" (الكبيرة) have ال (the) attached to it?

In Arabic, an adjective must perfectly match the noun it describes. Because "the tree" (الشجرة) is a specific, definite noun starting with ال, its adjective must also be definite. So, Arabic literally says "the tree the big" (الشجرة الكبيرة).

Why is the feminine form of "big" (الكبيرة) used if the cat is masculine?

The adjective is describing "the tree" (الشجرة), not the cat (القط). The word for tree ends with a "taa marbuta" (ة), which is the most common marker for feminine words. Because the tree is feminine, the adjective describing it must also end in ة.