[Coda]

-chatta is slang for -te shimatta. (It'll occasionally become -jatta in the presence of rendaku, although this seems to be less predictable than normal rendaku.) Literally it means "~ finished". You use it to refer to an action that's already happened but you're regretful/disappointed/otherwise negative about that fact.

牛乳を落としちゃったら、泣かないで。

If you drop the milk, don't cry.

On the -nakya lesson, other equivalents are "~nai to ikenai", "~nakute wa dame" (and equivalently, "~nakya dame" / "~nakucha dame"), and of course you can always go more formal with "ikemasen" instead of "ikenai". The negation is to put the base verb in -te form instead of -nakute form, so while "shinakute wa ikenai" is "must do", "shite wa ikenai" (or "shite wa dame", or "shite mo dame", the nuance between the two is subtle enough that you don't need to worry about it much) is one way to say "must not do".