Which database tables should I edit, and which PHP/JS files should I change to add a custom text field in Add Topic form?
I'm really sorry, but we cannot answer this question with simple 5-6 sentences. This requires deeper a support. The feature you are asking cannot be reached by making a simple customization.
Please note, that we don't provide support for such customization, we may help in 1-2 simple questions related to colors and background but not more. We only help with general questions and issues.
Thank you for your understanding.
Currently we have a plugin customization and custom addon development services at gVectors Team. They can asses the work and create it for you. Just contact us via sales[at]gvectors.com email address and send a list of requirements you'd like to have.