Believe it or not the war was immensely popular in Russia(at least in 1914),So much so that a commentator said that the Tsar is once again master of his people body and soul or something. The Italian government have additional causes to be fear too,The Libyan war of 1912 despite only token Ottoman resistance undo 50 years! of fiscal prudence and badly deplete their manpower and equipment!.In truth the public got little to do with the decision to enter the war anyway it was the King and his foreign minister sidelining the parliament.

You forgot the fact that Italy was offered one of the irredenta provice for neutrality,The government have any number of ways to spin it as diplomatic victory(Which it is). The economic rich that flow in would satisfy the population too.

The majority of the population didn't want war though, It just some nationalist group that were really loud.

I think the Austrian were justified against Serbian terrorist state though,It's like US response to 9/11. Although in hindsight this was stupid thing to do.

Austria-Hungary did have a formidable navy with several Dreadnought though.

The things is they were already offered one of their coveted Austrian province by staying neutral . To bad this is not enough for the King and the hardline nationalist,Just look at Spain and the US who profited so immensely for the war. By staying neutral Italy could get a free province and fill up their treasury with Gold and could have build up their industry with foreign money.