Is it normal to have eating habits like these?

You need to go see a doctor, who would hopefully send you to a psychologist and (if you are ok verweight, which may not even be the case) a dietitian. They can help you be healthy.

It appears that you are losing self control and regaining it. If this is the case then it's perfectly normal.
To maintain a good weight and health what you eat us more important than how much you eat. A diet plan suitable for you will easily be available on internet.
The way you have dieted earlier is harmful to health.

Thats exactly what happened to me. I really wanted to get rid of my belly, so I started calorie restricting. Of course I lost a lot of weight, and because I was constantly hungry, I would feel depressed all the time. I stopped being socially active at school and online, and when the hunger became too much to handle, I would binge eat. Them I would starve myself to get back all the weight I gained. I guess you could say I am anorexic, or bulimic, I don't really care about the labels tbh.
All I know is that my health is definitely at risk, since I've been losing hair and stopped having menstruation because of my lack of vitamins, so I am trying to recover from this eating disorder. It's difficult though. It's like an addiction. Starving myself and seeing myself get thinner as the day passes is satisfying, but when I do eat a good amount of food, I would feel extreme hate for myself.
I hope you try to get back to eating normally because dealing with eating disorders is like being stuck in a dark cell with no way out.

Yes it is normal but not healthy not at all healthy.

People (women and feminine gays) obsess about their weight when they don't need to.