No. Well, sort of, sometimes. You can't say "The chair is about the table" or "The boy is about the tree". "Near" is the word you want in these instances. You can say "He's about somewhere", meaning he's nearby you're just not sure where exactly right now. Equally if someone is looking for something that you know is somewhere near, but you are not sure where exactly it is, you can say "It's somewhere about".

You can use "about" as a measurement between two things for example "The apple is about 1cm away from the orange." But you cannot use it to show the distance between two items.

No