So when it becomes a copy of that blanked creature, does the Impostor also have no abilities at that point - since it become a copy of a creature that at the moment has no abilities?

The use of blank seems ill-advised here.

No, copy effects copy the creature's printed values and basically* nothing else. This steals a creature's abilities UEOT.

*: The exceptions are copy effects that modify how something's a copy. So if you have a Phyrexian Metamorph copying my Runeclaw Bear, it's a 2/2 green artifact creature; and my Clone of your Metamorph-Bear is also an artifact creature. If you have a Quicksilver Gargantuan copy of my Spikeshot Goblin, my Clone can be a 7/7 Spikeshot too. Other more interesting copy-modifications that can be further copied are Progenitor Mimic and Vesuvan Shapeshifter.

Sure.

IMO the main point to take from this is that the answer to that question isn't immediately obvious and the issue is caused by the presence of blank. While I personally don't think the keyword in question is in itself problematic, I wouldn't encourage it to used in this way (that raise complex rules questions).

Blank seemed like a great way to show a lost identity, which led to this top-down design of someone who steals someone's identity. That seemed like a great fit with the cyberpunk aspects of the plane.

I was worried that Anonymous Imposter's copy ability wouldn't copy the blanked creature's abilities, which was the whole inspiration for the card.

If you don't know the answer to a rules question, that should be a warning sign that you cannot generally assume players to know the answer either.