Adding (subtraction is special kind of adding) and counting from 1 to 4 are skills "hardcoded" into us. More over we solve this kind of problems in different part of brain then "rest" of math. So everyone can count from 1 to 4 but not everyone can say that.
The computer voice says the sentence as if it was a question. Google translate is a little better
I thought it meant "Each human knows to count." This could refer to gambling as well xD
Yes, this is translated very literally as "liczyć na kogoś" (na + Acc).
There's a saying "Umiesz liczyć, to licz na siebie" - You can count, so count on yourself.
Is the difference between mogę and umie the fact that mogę is "I can" whereas umie is "can" in general?
"mogę" is 1st person singular (as you wrote), so perhaps it makes more sense to focus on 3rd person singular "może" here.
"może" would either mean that he/she/it is allowed to, or at least 'able to' do it.
"umie" means that he/she/it 'knows how to do' something, possesses the knowledge and skills. Like "Mój syn ma pięć lat i już umie czytać" = My son is five and he already [knows how to/can] read.