You can write both תקרה and תיקרה. You can always add extra י and ו to clarify the vowel. This won't be considered a spelling mistake, and this is actually called "כתיב מלא" (ktiv-maleh = "full writing").
Does Duolingo understand this? It's often marked wrong or "almost correct"?
It may not be referring to a leak. Water may have condensed on the ceiling and be dripping off.
טפה tifah means "drop, a little, driblet" There is a word in linguistics "reduplication"--an initial syllable or, as in this case, the repeating of a root word, to make a new word. So multiple little drops = drizzling. It's also an example of onomatopoeia (a word that sounds like what it means)