I will keep it brief yet impactful. Are private scripts considered better or safer than published scripts that anyone can use? Are the ban rates very low?

Was unable to find anything on search. Is there a way for me to run the patched runelite dream bot and a non-patched runelite dream bot simultaneously?

9 times out of 10 it gives the malformed packet error because it's hopping worlds via disconnect, which typically is faster than using the world hopper in game. Malformed is just the generic error you get when it does this for Jagex Accounts. For the odd instance this isn't related to world hopping it's usually hopping due to lag, or is genuinely disconnecting. Either way, post in the Discord server so it can be looked into.

Which quest is it doing it for?

This one should do it