If you're in the first world then chances are you've already 2000+ calories today and don't really need more. You're hungry before bed because your blood sugar is falling, and all those extra calories will do is push you over the limit for the day, aka extra calories lead to fat.
I think you are making the assumption that eating before bed implies an extra snack, but it could just be that you have dinner shortly before going to bed.
RESULTS:
During sleep, casein protein was effectively digested and absorbed resulting in a rapid rise in circulating amino acid levels, which were sustained throughout the remainder of the night. Protein ingestion before sleep increased whole-body protein synthesis rates (311 ± 8 vs 246 ± 9 μmol·kg per 7.5 h) and improved net protein balance (61 ± 5 vs -11 ± 6 μmol·kg per 7.5 h) in the PRO vs the PLA experiment (P < 0.01). Mixed muscle protein synthesis rates were ∼22% higher in the PRO vs the PLA experiment, which reached borderline significance (0.059%·h ± 0.005%·h vs 0.048%·h ± 0.004%·h, P = 0.05).
Yes. Aside from increasing odds of acid reflux, the digestive process raises core body temperature. Typically body temperature must go down for optimal sleep.