1) - That is either Crop or Clear Color: Crop -- draw a shape over the photo/image, this can be any shape not just a rectangle or oval, adjust the shape for the portion to "keep" (this is what is powerful, you can zoom in and adjust very precisely at your convenience). Then select the shape and the image and execute Crop. Everything "outside" the shape is removed - becomes clear.
1) -- Or use Clear Color, that is a bitmap approach, the edges will be a little more jaggy, cropping is the better approach and a lot easier to manage in most causes.
2) No, not a all. EazyDraw is a vector drawing program. You can cut things, then delete portions after the cut. Knife is a vector drawing tool, Eraser is a "paint" program tool. No "Eraser" in EazyDraw - but Crop and Clear Color are similar and really easier to use to get a clean precise edge (remember to zoom in - a lot).
3) Sure - Open Layers drawer, near the bottom see "Enabled Actions", all possibilities for viewing layers, selecting, or hiding layers are there, use that in conjunction with the "ON" check box on the Layers Table which is near the top of the Layers area. Open "Layers" from the top of the Format main menu. If you are new to layers be sure to watch the videos on the topic, start with the one on Drawing Order then move on to the Layers videos. Layers are not quite the same in EazyDraw as they are in the older technology illustration programs - you don't need Layers to composite or export your images, they are just a tool aid drawing of more dense graphics or as "overlays" -- so don't jump into Layers unless you kind of know why you need them.
4) You may want to get a Paint program too, EazyDraw will be your vector drawing tool. In general you can create better quality images much more efficiently with vector, but it does depend on project. Painting is more tedious but good if you need images with softer appearance that will be used for one particular use most likely for "small" or low quality use.