"Unfortunately the owner was asking more than they were willing to pay." is correct. If you substituted "asked" for "was asking," the sentence would be grammatical but awkward-sounding, in this context. "Was asking" is the verb you'd expect to find here.

Was asked or got asked?

Both sentences are possible, but the word order is unusual. I prefer "was asked", but "got asked" is possible. It would be easier to allow the student to be the subject of the sentence: My student asked me this question. Passive sentences are often wordy and awkward.

When we use ask or asked?

Use “ask for” with the object you want to receive: I asked the teacher for a pencil. I asked her for a glass of water. My son asked for a video game for Christmas.