Web Cam Legibility

Hi,

I'm a private Math tutor. Because I traveled outside my country for some months, I will need to connect to my current students, online via Skype, to finish with them before exam time & because of this, I'm going to buy a laptop (the first laptop in my life in fact!) and I'm almost settled on a MacBook Pro but I'd like to ask about 2 things first:

Is it possible for the built in web cam to show the handwritten work of my students on paper in a legible way? (this is a crucial part in all my lessons where I need to check their work when it's time for them to do Math after explaining the concept)

Is it possible to evade using the mouse to explain in a written manner what I'm trying to explain? for example, Is there any hardware/software that can let me write my explanations on virtual paper so that my other students see & hear what I"m explaining in real time?

Many thanks in advance...