Yes, this is a "wagon." https://imgur.com/DjIBifo.png "Wagon" is also applied to other four-wheeled vehicles pulled by horses, mules, or oxen. I am not quite sure, but I think "wagon" may technically refer to the arrangement of four wheels, in which the two front wheels are mounted on an axle that is connected to the long pole or handle by which the wagon is pulled. Full-sized wagons are on farms. In the United States, part of our cultural semi-mythology involves the "covered wagons" on which settler traveled West in the days of the Oregon Trail, the early 1800s: https://en.wikipedia.org/wiki/File:Covered_wagon_at_the_High_Desert_Museum_Outside.jpg

Yes, the answer would be a "wagon" or more specifically a "toy wagon" in American English. "Cart" often refers to the thing you push around a grocery store or supermarket. "Trolley" most often refers to a tram or other type of public transport (often for tourists) in places like New Orleans.

In AmE it's wagon

yes it's a wagon, also it's used to carry things. Carts used in malls mostly and trolley to carry babies.