Learn English – Meaning of “give me chills”

"Good thing he has you!" is slightly less formal and more colloquial than "It's a good thing he has you." Both are grammatical and equivalent in meaning. "It's a good thing that he has you" is grammatical as well, but sounds a bit stilted; it's a bit too correct, and not the sort of thing one would expect to hear from a native speaker.

"Give input into" and "give input on" have different meanings. To give input into something is to provide information or resources. I would give input to a computer program, or perhaps give input to a machine.

To give input on something is to offer suggestions or opinions about the topic. In your example, the U.S Department of Education has opted not to offer suggestions about public parks, only school playgrounds. The input here isn't for the literal object (e.g., parks or playgrounds), but rather for a discussion about the object.