Congrats for being a successful student entrepreneur.
Building websites, providing services and selling web sites are business activities for you. Hence, income from such activities will be assessed under the head : "Income from business or profession".
As you don't own a company, the entire income is perhaps received by you in your name. It is a proprietary business for you. As the services are rendered by you from India, the services rendered to clients abroad are considered to be export of your services and are taxable in India. If you have to pay any taxes abroad, you can claim tax credit under DTAA (Double Taxation Avoidance Agreements) with such countries.
All reasonable expenses attributable to your business can be claimed as deduction from your business income. Apart from this, you can claim deductions u/s 80C, 80D and likewise.
You need to maintain books of account, which include cash and bank books and ledgers. You can maintain your books on computer system and e copies of invoices are ok.