Is it normal to both binge eat and food restrict?

The most important thing when dieting if weight loss is the goal, is to maintain a caloric deficit over time. When and what you eat is less important.

What do you mean "is it possible." Lots of people do this. Most of them don't have consistent accessibility to food or have an eating disorder (anorexia binge-purge subtype, bulimia, EDNOS, binge-eating disorder). Some people do OMAD ("one meal a day") or some variety of intermittent fasting that somewhat resembles the binge/restrict cycle but in a more "controlled" sense, and without some of the characteristics "behaviors" of an eating disorder (vomiting, laxative abuse, overexcercising.)

Yes you can binge eat while food restricting, people can do anything, try to throw a cat in the air and it'll land on you on its feet almost clawing your eyes out, even though its intention is to fall back in your hands, another possibility. I can certainly binge eat Kentucky Fried burgers and still restrict to no more eating (I eat 3 of them at once), and I eat three of them for the fun of it, just to show off behaviour you wouldn't do if you thought it was wise to eat one, I suck down those bad boys with a whole 2 litres of Pepsi Max, I take the trouble eating three of them at once, wiping my mouth with the Australian flag and burping very loudly above soft drink getting as much of it in my liver as I can, given that it's too much I can only drink half a 2-litre Pepsi Max and it's worth the money going home eating three Kentucky Fried burgers.