With the increase of difficulty throughout the game, do the number of monsters also increase? Like the amount of them in a packs? I couldn't find anything that told me the difference in 4 levels as far as monsters increasing in pack size.
No, the number of monsters does not change with difficulty, only the stats of the monsters. If you play the same part of an act on various difficulties, you should be able to tell that the number of monsters is similar in all of them.