I agree that "providing" is in common usage but it still seems incorrect to me. "He will be providing food for his family provided that he works hard."

Is someone, who can't type capital letters, capable of appraising others' work, I wonder?

"Providing he uses his brain." I know this phrase should be "provided (that) he uses his brain" but can somebody please explain why, in terms of parts of speech? As a native English speaker I usually know intuitively what is

His version is perfectly all right. In fact I'd say that it's more acceptable than the first because he has not split the verb structure.

They both make sense but they do not have the same meaning.

I wouldn't use 2 or 3 and, in any case, it's referring to a comment/observation and NOT to a decision. (The decision to fire or not to fire has not been made.)

1) Yes. 2) That's not an expression that I recognise. We sometimes say "Thanks to all" meaning "thanks to everyone".

Both passages contain grammatical errors which suggest to me a newspaper or magazine source. However, some Scientific journals lack strict accuracy so I can't be certain.

Note that that is slightly colloquial (contracted as we would speak it) and the correct sentence should be:- I wish that people would stop fighting each other all of the time.