Correct: Then, I ate breakfast and I brushed my teeth.

Explanation: And is a coordinating conjunction. We use and  to connect two words, phrases, clauses or prefixes together.

Mary: I studied lots of Math.

Correct: I studied a lot in Math.

Explanation: The phrase "lots of Math" is a little bit confusing so let us use  "a lot in Math" instead.

Mary: Then I came back to home.

Correct: Then I came back home.

Explanation: A number of nouns are followed by to. These include nouns expressing direction or destination such as door, entrance, road, route, way. Home is not included so we only say "I came back home."

Mary: Then I studied with teacher Monica I did my homework.

Correct: Then I studied with teacherMonica and I did myhomework.

Explanation: And  is acoordinating conjunction. We use and  to connect two words, phrases, clauses or prefixes together:

~Hello, Mary! Wow. I can see that you did a lot of things today. It's a good thing that you study hard in Math, and I hope in English, as well. It's 20 days before your birthday. I am excited about it. I'll see your again tomorrow. Thankyou for studying with me. Good night, Mary. *(^_^)*