1.
Chanjong: I do a lot of activity's.
correct: I do a lot of activities.

*The plural of activity is activities. Be mindful of the correct plural form of nouns. Apostrophe s ('s) is put before or after s to show possession.

2.
Chanjong: In subject I do math.
correct: I study math.
correct: I do math.

* I rephrased your sentence.

correct: I study math subject.

*This one is also correct though it will sound repetitive because as we know, math is a subject. But I asked you to make a sentence using the word "subject".

3.
Chanjong: I show respect.
correct!

This one is considered correct or you can add more.