This last point is important: It's been noted that children on make certain types of mistakes, but don't make others. For example, when learning do-support, which is when you take a sentence like:
(1) He wants to go to school.
And you make it a question:
(2) Does he want to go to school?
Children do not make the mistake of learning a "put do one spot to the left" rule and instead always learn a "put do at the beginning of a sentence" rule even when all their input satisfies both.
Based on this, it's been argued that there are some grammars humans can learn and some grammar humans can't learn, regardless of the input. These constraints on what constitutes a possible human language are part of UG.