Whiteboard animation: how to zoom and draw a motion?
Erase and redraw

If you play the first video frame by frame (by pausing the video and pressing the left or right key) you see that moving objects are erased and redrawn again and again. The line properties (thickness, straightness) change a little bit between frames, hinting that the line is redrawn each time (best seen at 0:45). 

Camera motion

About the 2nd video you're correct that manually moving your camera will be not so smooth. If you have a jib you could achieve much smoother motion. 
However, I don't think they used that in this video. The biggest output size is 720p meaning that the frame has a size of 1280x720 pixels. If you have a camera that can film 1920x1080 pixels you have quite some room left in which you can crop and move the frame.