I drop by my unbrella friend's house.
After a while I will be doing my homework.
There are lots of homework.
 I'm riding bike right away.
I finished my homework just in time.

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1.
Alice: I drop by my unbrella.
Correct: I drop by my unbrella friend's house.
Explanation:
*drop by - visit a place for a short time
*An umbrella is not a place.

2.
Alice: After a while I was doing homework.
Correct: After a while I will be doing my homework.
Explanation:
*after a while  means later or at some time in the future
You should not use was because it indicates past action.

3.
Alice: Lots of homework.
Correct: There are lots of homework.
Explanation:
*If your sentence doesn't have a subject, start with the phrase there are.

4.
Alice: Right away I'm riding bike.
Correct:  I'm riding bike right away.
Explanation:
*Use the expression right away in the end part of the sentence.

5.
Alice: I finish my homework just in time.
Correct: I finished my homework just in time.
Explanation:
*Just in time means just before the last minute, so the action happened already. Use the past tense of the verb.

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Hello, Alice! Thank you for submitting your homework. Please read the following corrections and explanations carefully. If you have questions and clarifications, you can ask me in our class. Thank you!