School prestige on return offer rates?

UK perspective - if anything, offers might be higher for non/semi-targets. It's quite easy here for Oxford/Cambridge/Imperial/LSE people to sneak through interviews by virtue of university name, knowing some basic financials, and being used to behavioural questions. The people who make it through from true non-targets (not Durham or Edinburgh) are often genuinely brilliant and will be the top performers in their teams.

And yes, return offers are mostly performance (and fit) based. 

Performance. the only way that school impacts return rates in my experience is if there's a big pipeline from a certain school- say, Dartmouth- and all the Dartmouth analysts/associates/VPs push for the dartmouth interns to get return offers, or are even just subconsciously biased and are more friendly with the kids from their school and then vouch for them more. This is just as much the case (even more so, sometimes) if there's a strong pipeline from either a semi-target or a non-target, as these alumni often look after each other even more than target alums. Other than that, I don't think anyone considers school prestige. 

School = Interviews/network

Skills in Interviews =  Offers 

Typically students at non targets also have a higher degree of preparation in interviews due to the fact that many of their collogues also get interview thus they can "compare notes".  

Yes school name matters. If anything it at least program your interviewer subconscious to think that if you went to Oxbridge you’re at least half decent 

I don’t think it matters. Once you are there as long as you can do a good job and try your best I think you’ll be fine. Hopefully though. Not sure if any of your deal teams may know where you went to school even and/or care. Work is work. College is college. It’s not that big of a difference where you went to school once it’s time to actually get work done in my humble opinion. Good luck 

It doesn’t matter. Assuming you’re not in a group/bank that purposely overhires interns for few limited full-time spots (which is pretty rare), your school won’t make a difference.

You’re simply fighting for your own full-time spot, so your performance/personality is significantly more important

As far as the final round table goes, no, I do not believe that school is a factor.
However, there are other ways that school might impact return offer rates. If your school has a large pipeline at the bank, you will probably have planned alumni events throughout the summer. Alumni might try getting feedback on your performance throughout the summer and then work with you to address any issues. The alumni group is also an extra network you have at your disposal to get advice on securing a return. Finally, an alumni in your group might be more likely to go to bat for you. 

I’m sure it helps but only so much. In my intern class, Penn and Cornell had ~60% return rate, while my semi target was 100%. I think it’s more important to have a good alumni network at the bank. My schools recruiting and retention shot up cause we had an MD pulling for everyone behind the scenes but also helping us make the right connections and perform well