I want to get into what KVD does: bigger spinning reels for better line management and casting distance. The 35 is obviously a bigger reel, meant to hold bigger line. But will 15 pound Power Pro braid work well being that it's 4 pound diameter?

If you are going with braid a 35 size reel is too big honestly, the better line management is noticed when using mono or fluoro lines since a wider spool creates bigger loops in the line which tend to not want to jump off the spool as much. Using braid all but eliminates line management issues on spinning reels, so you can get away with using a smaller reel. With 15lb braid I'd go with the 25 size. 

It will work fine.  Use backing or it will take a lot of 15# braid to fill that spool.  Also be conscious of your drag if you use a light leader.  That size real probably has quite a bit of drag.

Fill 2/3rds with #8lb. mono then the last 1/3rd with #15 lb. braid (or roughly 65 yrds. with braid) then tie on a #8lb. co-poly or FC leader... That #35 series reel would be good for a shaky head , weightless Senko , etc.

Disclaimer: I fish with Pflueger Supremes not Presidents and I use reel sizes 25, 30 & 35 all are loaded with 8lb PE line.  Which size reel mates with which reel is determined mostly by which reel balances the rod best and to a lesser extent reel gear ratio.  I believe both the reasons you are stating to justify your reel size decision are better influenced by the line you choose to fill the spool.

 

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The whole idea of the larger spool is to handle 6# etc Fluoro. Non issue with braid. 

What length of rod. A 3500 size reel will have less line issues, on a rod 7ft or longer. The first guide should be no smaller that 50percent of the spool diameter.

What's rod length have to do with it? The reduction train (first 3-4 guides) are critical on a spinning rod. The larger diameter guide is to get height actually but we're getting into rodgeek territory. 

I am trying to think if I ever used  15# braid on mine or not. Anyway, 15# braid should be fine on that reel, just be sure to use a fair amount of backing to not waste line you don't need. I bought 15# braid to put on it this year, just ended up putting it on another reel so I'll have to buy some more at some point. According to Pflueger's line ratings, it is rated for as low as 8# braid.

 

That said, I would of with a smaller reel for finesse fishing. My Daiwa BG 2000 holds much less line but has a similar diameter spool for what it's worth and a 2500 sized BG should have a larger diameter spool while holding less line.