If you create labels in-house as indicated in post 1, you need to outline the procedure that you use to create them. To Scampi's point, the procedure needs to ensure the labels meet regulatory requirements.
But in post 3 you mention that you do pack private label for some customers, and that gets just slightly stickier. If you help with the raw creation of those labels, you need a procedure that shows how you do it, how you ensure they meet regulatory requirements, and how they meet customer requirements (the process for them being approved). But if your customer provides their own private brand labels, your procedure needs to outline how you check them before use (again checking for accuracy, regulatory compliance, etc). Document the methods you use to ensure the correct labels are used for the correct items.
Back in my spice days, we would grind/blend/repack spices into case size quantities for B2B sales, and we were a 3PL. The case labels were printed in house on regular Avery half page stickers we could print ourselves, super simple look and procedure. We'd email a word doc template to the material owners for approval (their naming, lot code, production date, distributed by info, etc). They'd approve it via email, and that label template along with approval email went into the paper batch record.