The 2.4 is noticeably larger than the 2.3 HRII. It’s not only the casing, the knobs too are larger. Since you’re using it as a rear tire, I’d probably stick with the 2.3.
As for the compound MaxxTerra is the name for Maxxis’ 3C trail compound (I know because I named it when I worked there). The 3C MaxxTerra has better grip than the dual compound, but it’s also going to wear faster. Again, since you’re looking at it as a rear tire, I would go with the dual to save a few bucks and get better tread life. Up front is really where you want to splurge for ultimate grip.
Many riders will purchase a dual compound tire for the rear and a 3C for the front. When the rear wears, move the front tire to the back and replace it with another 3C.
No. Just buy the correct sized tire in the first place. Cutting down center knobs is one thing – if you’re a racer and getting tires for free – but side knobs? No way. Why spend money on good rubber if you’re just going to cut it away.
One manufacturers 2.4 is not the same as another’s. Measurement methods vary. Maxxis tend to be large volume relative to their stated measurement while Contis tend to be average to low volume relative to their measurement. You may well find that the HRII in a 2.3 is a wide or even wider than the Conti Trail King 2.4! I’m running a 2.4″ HRII on the rear of one one of my bikes and Trail King 2.4s front and rear on my other bike and the HRII is noticeably wider than the “same size” Conti.