Consume Product

That's a dip pen. Similar to a fountain pen, but lacking the internal, refillable reservoir. Do you see the ink well on the left side of her desk, next to her right hand, her writing hand? Dead giveaway.

Here are some examples:
https://pomf2.lain.la/f/ev03lpkb.jpg

that's one ugly yenta

Not sure but you can buy you very own version of Otto Frank's pen here: https://peppercave.com/shop/ols/products/ottospen