Yes, that is what the experience of most people is like without aphantasia. I can even, for like a second, see a fully formed picture in my mind, like a scene from a sci-fi movie, or anything else, really, although it can disappear if I don't focus on the exact details. I can see everything, the shapes, the layout, colors, all of it. It really is like playing a movie in your mind.
Sure, I can count them. I can make them hexagons or pentagons at will when I think about them. It does take some time however to remember what a soccer ball actually looks like but after that I can see every details of it.
How do I know how detailed you are experiencing a mental picture? Can you imagine a detailed map and follow a street from one place to another in precise detail? Or is it an approximation
Yes, it's pretty accurate. Interestingly, this can be used as a memory technique, the method of loci, also known as the memory palace. You imagine a path such as from your house to the grocery store, and you place items on that path to remember them. For example, a large fish cresting out of the sidewalk might remind you to buy fish at the grocer.