HDR option should be used when one needs a detailed picture of something or someone. For example, one takes a pic of a sari, then zooms out the pic to see the embroidery on the sari. An HDR (or HR or HD) pic will show a whole lot of details and would not pixelate (would not blur very quickly while zooming). Another example, one takes a full length pic of any person. Suppose it is a HD pic, then it can be zoomed out to see even a mole on the face. A normal (non-HD) pic will pixelate when zoomed out and would not show the finer details.
HDR pics are heavy files as they contain a lot of data. It can be anything more than 2MB in size depending on the details it contains. The pixel size can be anything more than 3000 on the larger side. The file size will go on increasing with every edit in any software like Photoshop etc, but the pixel size will always remain the same until it is changed intentionally.
The lightning sign is for the flash, and should be used as explained by Mahesh
Turning of the white circle to green (it can be a square also in some models) - It is the process of focusing of the lens. Green color signals that the lens is properly focused and the camera is ready to take the snap of the target. So, when one needs to take a pic, one needs to turn the camera on, then needs to tap on the screen, immediately a white circle or a square appears on the screen. The camera (the lens) starts focusing on the point where the photographer has tapped. The lens will try to bring out the best out of the area which has been tapped. The circle or the square will turn green when the targeted area is properly focused and the camera is fully ready. Take the snap at that time.
Reason for the need of the multi tapping:-
1. Maybe you are not waiting till the circle turns green and tap it again. It tells the camera to focus again. So the whole process starts again.
2. Or, you are taking the pic in HDR mode. In that mode, the camera or the lens will take a longer time than usual to get ready as it is taking in a lot more details of the targeted area. So, you might be tapping it again before the white circle turns green.
It is like giving multi commands to a slow computer. The computer will get even slower.
About the selfies, sharpness and the camera resolution:- My views are that as a beginner, one should not try to change the factory settings of the camera. The factory settings are good enough for all the normal things. First just get familiar with the functioning of the camera properly, then try experimenting. One may need to take the phone to the service center for a software update or reloading of factory settings if one makes a mistake.