Your only mistake is a missing "et" in "trente-et-un".

Here is how these numbers are written in the traditional way which is still accepted as correct and the most commonly used:

198 647: cent quatre-vingt-dix-huit mille six cent quarante-sept

318 431: trois cent dix-huit mille quatre cent trente et un

2 857 566: deux millions huit cent cinquante-sept mille cinq cent soixante-six

Since the Dec 6, 1990 rectifications, connecting all components of a numeral with dashes is allowed, albeit not mandatory:

198 647: cent-quatre-vingt-dix-huit-mille-six-cent-quarante-sept

318 431: trois-cent-dix-huit-mille-quatre-cent-trente-et-un

2 857 566: deux-millions-huit-cent-cinquante-sept-mille-cinq-cent-soixante-six

However, depending on the sources, million and milliard are subject to that simplification or not. The "Académie Française" is recommending:

2 857 566: deux millions huit-cent-cinquante-sept-mille-cinq-cent-soixante-six

Note that you do not use a comma in French to separate thousands, the comma is exclusively used as a decimal separator where English uses a dot.

Note also that while "quatre-vingts" takes an ending "s", there is no "s" in "quatre-vingt-dix-huit" so your form is correct.

"Cent nonante-huit mille" is used instead of "cent quatre-vingt-dix-huit mille" in Belgium and Switzerland.

Finally, your last guess is also correct as "million" is a regular word so must take the plural form in "deux millions …"