Learn English – What’s the difference between ‘addictive’ and ‘addicting’

These days, "press" would have a strong traditional-media connotation, likely excluding bloggers, since new-media publishers neither own nor use industrial printing equipment. "Media" would include basically anyone who writes or speaks for an audience.

Nothing really. In English you tend to get a lot of words that mean the same thing, sometimes there are historical or poetic reasons for choosing one word — but not in this case.

Other than big being a much more common word and large sounding more refined there aren't many areas where you would use one over the other for purely grammatical reasons.
Note that big can also mean "major or important" — so big decision, big spender.