Kapının altındaki çatlak suyun içeri sızmasına neden oluyor.

We can break kapının altındaki çatlak into these parts:

• kapı “door”
• -nın genitive suffix → kapının “of the door”
• alt “bottom”
• -ı 3 sg possessive suffix → altı “its bottom”
• -nda locative suffix → altında “at its bottom”
• -ki relative-locative suffix → altındaki “that which is at its bottom”
• çatlak “crack”

Put together: “the crack that is under (the bottom of) the door.”

suyun içeri sızmasına splits as follows:

• su “water”
• -yun/-un genitive suffix → suyun “of the water”
• içeri adverb “inside”
• sız verb root “to seep/leak”
• -ma noun-forming suffix → sızma “the act of seeping”
• -sı 3 sg possessive suffix → sızması “its seeping”
• -na dative suffix → sızmasına “to its seeping”

Literally: “to the water’s seeping inside.”

Because the verb phrase neden olmak (literally “to become a cause”) requires its object—the event or state being caused—to be marked with the dative. So “the crack causes the water to seep inside” becomes “çatl‌ak suyun içeri sızmasına neden oluyor.”

• neden is a noun meaning “cause.”
• olmak means “to become” or “to happen.”
  Combined, neden oluyor literally means “it becomes a cause,” i.e. “it causes (something).”
  You could use sebep oluyor (“it creates/makes a reason”), which is almost interchangeable, but neden oluyor is very common in everyday speech.

Insert bir before çatlak:

• kapının altındaki bir çatlak
  This clearly means “a crack under the door” rather than a specific, known crack.

• içeri is a pure adverb indicating direction (“inside”).
• içeriye is the dative form of içerisi (“its inside”).

Both can express movement toward the interior, but:
• For fixed verb+adverb collocations like içeri sızmak, learners almost always use the adverb içeri.
• If you want to emphasize the destination as a noun phrase, you could say suyun içeriye sızmasına (“to the water’s seeping into the inside”), though it’s less common here.