In order to control my product from the web, I need to implement a GPRS modem in it?
For example, do cellulars comprise GPRS modem inside their enclosure?
Well the GPRS modem is just that, a modem. You'll still need to pay a monthly fee for the service. It's a really popular student project in India where I assume cell phones are cheap as dirt to operate.
Lots of links on the web. https://hackaday.com/2008/05/28/gsm-remote-control-project/