Yes that is fine as long as the mug is a plain one and has no distinguishing character like an emblem or logo on it. The suppliers who sell non branded mugs or Tshirts don't care what you do with them after you buy them.

You can buy product in China without brand. You can put your own brand and sell it as yours. Many companies do this especially in electronic products or computer parts. You will notice same construction (in and out) but different company names.

You need the sellers permission because the sellers logo would be on the shirt/mug. l

Providing they have no branding then you can sell on.

You can do what you like with them so long as no copyright laws are infringed.

This may sound a very silly question, but I was curious, can you buy basic products, like mugs or t-shirts, with no branding on them, and then you customize them yourself, and sell them on, is that perfectly okay, or do you need the suppliers permission?

Thanks in advance.