NO registration require for conducting non professional faculty coaching. 

Since you are staying in village approach local panchayat office for licence 

2) in state level you need licence under shop and establishment act 

3) if your turnover is crossing Rs 20 lakhs need GST registration 

To open a online a business there is no need to apply for trade license.

Whoever if your area is governed by Panchayat then this authority alone can issue such License.

For the time being only a bank account is required and nothing else. 

Trade license will be ok. Also see if you have some tax oblihatins

- You should approach to the local Municipal corporation of the area , where you are going to open the Coaching Center , for obtaining a Trade Licence. 

- Further, if you want to start a small scale Coaching Center , then there is no need to obtain a trade licence , but if you are going to start a big size , then a Trade license and pay tax for the revenue generated by the Coaching Center is mandatory.

1. For online coaching centre, there no licence required, EXCEPT registration with GST, PAN.

2. However, IF you are going to have an physical office, THEN you would be requiring Shop & Establishment license, Fire Dept & Police Dept. permissions  etc.....

All businesses are required to be registered under the Shops and Establishments Act with the inspectorate of that area.

You can apply for registration of the company under shops and establishment act.

You can prepare the details and approach the registrar office within your jurisdiction for getting your coaching center registered. 

See if it is online coaching centre no registration as such is required as you are not operating any establishment it shall be just informative website and lectures . 

1. If you are willing to open online coaching center then you don't need any licence from local authorities.

2. You will need GST registration if your turnover is expected to reach 20 lakhs per annum.