Learn Polish: Rura pękła i zalała kuchnię. - The pipe burst and flooded the kitchen.

Many perfective verbs ending in -nąć (which often describe a sudden, single action) drop that n in the past tense. So instead of saying pęknęła, the correct past tense feminine form is simply pękła.

Why are both verbs in this sentence in the perfective aspect?

The sentence describes a sequence of completed, one-time events: first the pipe burst (pękła), and then it flooded the kitchen (zalała). If you used the imperfective forms (pękała i zalewała), it would sound like the pipe was slowly tearing apart and continually leaking over a period of time.

Why does the word kuchnia change to kuchnię here?

Kuchnię is in the accusative case because it is the direct object receiving the action of the verb zalała (flooded). As a quick refresher: feminine nouns ending in -a in the nominative case always change their ending to -ę when they are the direct object.

How could I use the current lesson's conjunction chyba że (unless) with this sentence?

You could use it to offer an alternative explanation for a problem. For example: Ktoś wylał wodę, chyba że rura pękła i zalała kuchnię (Someone spilled water, unless the pipe burst and flooded the kitchen). Remember that chyba że always requires a comma right before it.