The first picture, right one: the pen is a bit like "Ming". The second pen on the left looks a bit like "Ming", but I'm not 100% sure about these two words.
In the second picture, the two words on the right are "Yi", the middle word on the left is "Jiang", and the first and third words on the left are hard to recognize. This is not a cursive script.
What kind of cup is this? Then we can infer it again. Another is that some people now add cursive characters when processing products because they love calligraphy very much and pursue the artistic beauty of Chinese characters, but people who make things don't know cursive, so some words are often wrong. These situations should be viewed comprehensively.
I'm teacher Li who teaches calligraphy and Chinese studies. I hope the answer will help you!