Do I need an Internet connection to make the calls?

If you are going to use an IP phone or software phone (softphone) the answer is yes. In the case that you only want to make and receive calls through your current operator’s mobile line, you will not need a broadband Internet connection since the calls will be made through your mobile phone.

More information on how calls are made can be found in the following article:
How can I make and receive calls with Monema?