(3) I want to use cartoons and animations (such as doodles). Which is best?
As Descent stated, the "MinutePhysics" style is quite simply great. People have short attention spans so you need to catch their attention ASAP.
Doodling is very good but you'll have to be extremely proficient at cartoon drawing and it is a laborious process, you wont be able to churn out quick videos like this.
An alternative to this which still retains the "doodle" feeling is paying a monthly fee for the following program, you can start a free trial to see if it is for you: http://www.videoscribe.co/
If you want to hand draw them, combine the camcorder I offered in (1) with a tripod. Position it over your shoulder and record yourself drawing. Please refer to my initial contention, this is deceptively hard and will limit the amount of videos you can produce in a specific period.
On the other hand, if you just want to make cool looking cartoons & use animations... you can use PowerPoint. PP is actually a very powerful tool when used correctly.
PP versions 2010 and above have a convert to WMV function so you can turn a PowerPoint into a video without too much hassle.
It's also quicker to make videos this way.
This guy creates all of his videos via PowerPoint, an example : https://www.youtube.com/watch?v=JZ-t_v8DgrI