Can you carry a laptop bag with you?

I'm flying to the US for 10 months next year. My question is whether I can take my carry-on luggage, backpack and a laptop bag in the plane. My laptop is a bit bigger and heavier and I'm afraid it will break. Which airlines would that be?

Laptop bag = a piece of hand luggage, if it can't be stored in a backpack. So, with three carry-on items, would you exceed the allowable carry-on amount on most (all?) Airlines. Otherwise, nothing speaks against carrying the laptop in your hand luggage.

Only thinks 1 piece of luggage as hand luggage. That's why I always fly with Lufthansa Buisiness or First Class. Since you may 2 pieces.

Some airlines allow in addition to carry-on luggage still a laptop bag. If not, then everything must fit in the hand luggage, which must not exceed certain size and weight classes. Is on the side of the airline what size and weight. Weight often specified less than 8kg.

Can I theoretically put the bag in the backpack and then put it out at the gate again?

If the backpack then does not exceed the dimensions and weight of carry-on luggage, yes.