When you borrow a house it's a rented house. This could also be a house for rent.

You can use 借家 in conversation to formally refer to a rented house or a house for rent. But it's more commonly found in legal contexts, like in laws and regulations.

This is a jukugo word, which usually means on'yomi readings from the kanji, but in this case 家 can be read with either the on'yomi or the kun'yomi. The kun'yomi here is や, which you learned with words like 空き家 and 大家, but here's a mnemonic in case you need help remembering it:

When you friend tells you they live in a rented house, you say, "So, it's a shack, yah (しゃくや)?" Wow. Pretty rude and judgmental of you. Thankfully, they reply, "It's a shack, yah. The place is really run-down." Huh, I guess it was a shack after all.

By the way, in the secondary reading しゃっか, the しゃく changes to しゃっ. This reading is mostly used in legal contexts though, so しゃくや is more common.