You work for your employer. You work in a building or an industry. You work at a business. You work on a project. You work with other people.

What are we making friend out of? Popsicle sticks? Aluminium cans?

Unmarried women go by "Miss". Married women go by "Misses". Divorced women go by "Mizz".

They could have meant to say "What's the matter." As in "What is the matter." but with a 'what + is' contraction. It could have been a typo if you read it online. What the matter is neither natural sounding, nor grammatically correct.

"Get people interested." "Get people to care about what is going on." "Raise awareness" is just fine.

You would say "when I was a child" to let the youth know that the time you are talking about is during your childhood. You would say "when I was a teenager" to let the youth know that the time you are talking about is during your adolescence, since "adolescence" is a big word for much younger people. These all appear correct except for #10. In #10, you should specify that they are "your elementary school years."

Yes. "What's" being a contraction of "what does." However, "what's" is also a contraction for "what is." Careful with these contractions.