Fun idea – thanks for sharing! I think any of these directions would make for a fun and educational project. Some thoughts/questions on each:

Do you have a good dataset with applied vs. basic annotations? If so, this should be pretty easy. If not, one direction would be to explore semi-supervised learning (Seb Ruder has a good blog post 3 on it).
This seems more interesting than #1 to me, but try to be careful with fairness and bias here. The model could easily learn to associate the race or gender of the the patent holders or the prestige of the organizations that they come from with the patent’s impact, since (I assume) these factors will correlate with citations. Removing bias completely won’t be possible, but it will add legitimacy to your project if you are careful & transparent about them. You wouldn’t want a scenario where companies use your tool to determine the value of their employee’s patents which would likely end up disproportionately rewarding men over women, for example.
After a quick google I found this paper 6, so I’d use that as a starting point and see what you could do that would be fun or interesting on top of that.