Zinc

No. Pretty much every modern engine uses rollers. Flat tappets need it to live, period. A viscosity of a higher number helps but the ZDDP is where its at....in the right dosage!
Diesel oil is overloaded with detergents, for our app.
A conventional or synthetic oil of the correct weight with the correct additive is best for a flat tappet equipped engine.

Yes! Over 2000 ppm (I'm not sure whether Zn or P, use Zn to be safe since it's ~10% higher) can attack camshaft lobes and cause catastrophic chunking. Be very careful with these additives. For example, ZDDPlus has 71800ppm Zn, 51500 ppm P. 30ml in 5qts will raise Zn ~450ppm, P300ppm. In a somewhat typical fairly weak 600ppm SM oil, that will raise Zn/P to "safe" levels of ~1100/900. Certainly add no more than 1/2 bottle (60ml) to get levels up to ~1600/1200. Remember, many Mobil 1s as an example are 900/800 at a minimum, HDEOs range from 900/800 (some CJ4s) to 1400/1300 (some CI4s).
STP was analyzed on the 1st page of the sticky of VOAs. It's <2000ppm undiluted and comes in a vehicle of very thick (~105 CsT @ 100 C.) oil. If you want to raise Zn/P carefully, use one of the more potent single-ingredient ones like ZDDPlus or Redline, know exactly what its' concentration is AND your oil's concentration, and do your sums carefully, recheck at least once. Too much of a good thing is very bad!
Maybe download (for $15) and read SAE technical article 2004-01-2986 "How much ZDP is enough", first.

Thats from the site I posted earlier.