Thank you for sharing the following conversations. The explanations below would help you to understand the following terms we used:

grammar:
Sun: I decide her academy...
Correction: I decide for her academy...

- It has to be with preposition to indicate the reason. The reason of the action is your "daughter." To whom do you decide for?

term "for" is used when we indicate reasons and use of something. (Ex: You decide for your daughter.)

Sun: All of this can be done only in on internet.
Correction: All of this can only be done in the internet.

All of this can be done ONLY ON the internet".

First and foremost, I would like to apologize for I missed use the word "in". And this sentence "All of this can be done ONLY ON the internet".
is also correct.

"Only" is an example of both adverb and adjective.
- We use only as an adjective to mean that there is just one or very few of something, or that there are no others

- We use only as an adverb to mean that something is limited to some people, things, an amount or an activity.

Sun: I have to teach my daughter math.
Correction: I have to teach math to my daughter./ I have to teach my daughter with Math.

"I have to teach my daughter math." is possible only if we put the preposition with. If you observe the sentence clearly The name of your daughter is MATH.

With is used to indicate being together or being involved.

With is used  to indicate "having":

Thank you so much for clearing this up, these following explanations might help you to poilsh more your sentences. Keep up the good work!