The OP writes:

<em>Then she asked me "how about this week?" and "how's your time?"</em>

In context, I’d say it’s short for, “please tell me how much available time for language exchange you have in your schedule this week, and be so kind as to give me an idea of what times would be best for you.” We often use ad-hoc short phrases that are ungrammatical, but make perfect sense in context. Personally, my preferred colloquial phrasing would be "how are you for time?", or more clearly, "what's your schedule look like?" You could even say "what's your week looking like?" (Etc.)

Neither of these is a normal question. I don't think that I've heard anyone say 'How's your day?', and I am pretty certain that I have never heard anyone say 'How's your time?'

During the day, you might say, for example, How's your day going? in the present continuous.

You might answer like this: "It's going OK. I'm quite busy, though."

At the end of the day, you might say How was your day? in the past simple.

You might say "It was boring. I just stayed home and studied."

I'm not sure what you mean by 'How's your time?'. Can you give some more context, please?

It could just be a brain-fart. Maybe the friend rolled out of bed a couple of hours too early that day?

Thanks for the context, Musik, but it's still not clear what this person is asking you.

Let's go back to the first question. She said "How about this week?" Was that a suggestion, for example:

"Let's have a meeting some time soon"

"OK. How about this week?"

I agree with you, Hazel. I don't think that "How's your time?" has any meaning as a standalone question.

Like you, I googled "How's your time?", and the only result was a Chinese film.

Can any Chinese speakers enlighten us? Is it a translation of a Chinese phrase?