By your own analysis, Israel should win against Hizballah. Hizballah attacked Israel without provocation, six years after Israel had left Lebanon completely. Do not make the mistake of thinking that Hizballah is fighting for Palestnians. They have their own agenda, and much of it is intimately linked with Iranian ambitions. Iran might have a strategic and theological reason for wiping Israel out, but it could not care less about the Palestinians per se, regardless of what propaganda they feed you.
At least 4 die in clashes between PKK militants, security forces in east Turkey (Reuters)
from the article: Firepower versus brainpower