I will buy a present for my mom.
I bought a pen.
So I will give it and kiss my mom.

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1.
Alice: I will buy a present to my mom.
Correct: I will buy a present for my mom.
Explanation:
*For means to be given to or used by someone or something.
*To is  used to give the reason for doing something.

2.
Alice: I bought a pen.
Correct: No correction

3.
Alice: So I will give it and kiss my mom.
Correct: So I will give it and kiss my mom.
Explanation: 
*So is used to connect sentences. You should never begin your sentence with a coordinating conjunction.

Example sentence: (correct usage)
Even though I added cream to the squid eyeball stew, Rocky ignored his serving, so I got a spoon and ate it myself.

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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!