For a bank note, you should use the numeral spelling "two hundred dollars".
The "I gave him two hundreds" is considering a "hundred" as a name for a 100 dollar bill, and that would imply you paid with 2 100 dollar bills, that is, not 4 50 dollar bills.
"two hundreds" can be used when a hundred X is a conventional size for a set of X's. For instance, when talking about white paper at an office, where bundles of one hundred sheets are kept. "I gave him to hundreds of white paper sheets".
The "I gave him two hundreds" is considering a "hundred" as a name for a 100 dollar bill, and that would imply you paid with 2 100 dollar bills, that is, not 4 50 dollar bills.
"two hundreds" can be used when a hundred X is a conventional size for a set of X's. For instance, when talking about white paper at an office, where bundles of one hundred sheets are kept.
"I gave him to hundreds of white paper sheets".
$2,000 - two thousand
$2,000,000,000 - you can write it any way you want
There are a hundred sheep in the fold.
two hundred two