What should I do after my DTV application was rejected and is there any impact on applying for a student visa?

Reject or cancel?

There is no appeal process, but you can certainly contact the embassy where you applied to try to get some clarification.

Keep in mind that the officers are looking for 4 main things.

1. That you are the person that you say you are (proof of identity).

2. That you possess the employment that you claim to possess, or that you are applying to a legitimate/approved course (proof of legitimacy).

3. That you have the funds that you say you have (proof of funds).

4. That you can support yourself while in Thailand (proof of income or finances).

...and of course that you follwed the directions in the application.

The decision has been made, and only thing you can do is to apply ( and pay ) again.

Next time apply with the full amount on your own personal account, no doggy sponsoring.

They wan’t to know you are an adult person, that can handle things yourself

Why dont you read the embassy website thoroughly before applying there are important information to be found both there and in the manual on the e-visa website top right corner.

No appeal process

There is no appeal process, You can reapply again as others have done. Applying for a student visa will not be affected. Seems your paperwork has a major issue going by the length of time to reply.

Absolutely no appeal mechanism available to you. You're going to have to give us a lot more detailed information on your submission scheme if you want an opinion on how to resubmit.