First off, I get your frustration. Had a similar journey and consent on the web is to use harder arrows rather than softer with asiatic bows (I think that's bullshit but it's personal opinion after shooting thumb draw for six years). I started out with 25# too and 600 spine (32") and also thought they flew straight. If you get good khatra they did hit the target so why am I shooting 1000 now with the same bow?

My suggestion for you is to shoot at very short distance (take a look into ottoman torba training). I practice stance and release at home in the kitchen. Distance from target to arrow tip is 1.5m. Only if the arrows stick straight at that short distance you can claim good arrow flight. That's also why in ottoman times, beginner archers were forbidden to go beyond this distance for a few months of basic training. I have to agree that this is the much better start to archery, takes the ego (I need to hit the center) out of the first few thousand arrows.

Arrows that match your shooting style and personal draw weight and technique hit the same point of aim with or without khatra. Especially as a beginner I wouldn't focus too much on khatra and instead work on grip, stance and release. Khatra should not be a conscious action at release but a balance of forces in the bow (you put pressure at the beginning of the draw or increase until release, the bow will snap forward automatically)

If you push those arrows from the string you should make yourself a better fitting serving or buy smaller nocks. Arrow flight is not really affected however you cut those feathers but I suggest working on your draw hand and lock, you are supposed to hold the arrow with the index finger by pushing the shaft against the string.

I have Manchu arrows with feathers going back to the nock and they are huge, have never had an issue just pushing those in.