So I want to add a series called, "Box" Series and there are 10 games in the series (That I know of). So I was wondering, Are you allowed to request a game before one you already requested gets accepted?

if you mean can you request a series before its accepteed, i think the safest bet would be to wait until it is. at least you know then

no i mean if i submitted a game 2 hours ago, and i submit another game before the first one gets accepted?

As long as you're not intentionally spamming them you're probably okay. If there's supposed to be a limit or cooldown or something, it should physically prevent you from submitting more, so I wouldn't worry about it too much.