At its core, Pulse SMS does not work any differently than the SMS app that came with your phone. Individual apps cannot make connections with your carrier, so all that Pulse SMS can really do is hand off messages to Android to be sent. Similar for receiving, Android will receive the message, then notify any SMS apps on the device.
The goal of Pulse SMS is to enable you to send messages, through your personal phone number, across all of the devices that you use every day. Basically, your other devices just forward information to your phone, where it is able to be handled and messages to be sent.
That means, if your carrier charges for SMS, then Pulse SMS will too. The same goes for MMS.
Does Pulse SMS create a new phone number for me or can I tell it which phone number to use?
No, Pulse SMS is going to use whatever phone number is on your phone. There is no way to create a new phone number. That is really the goal of the app: to be able to text from your personal phone number, across all of your devices.
Do my contacts have to use Pulse SMS to be able to receive messages from me?
No. Pulse SMS is a regular SMS app; your contacts can use whatever they want to send and receive messages to you. Pulse SMS provides no specific functionality when messaging between two Pulse SMS users.