India is split in two between the Europe and Pacific board. W. India (I think that is what it is called) is on the Europe board but counts for the UK Pacific income, correct?
No. All of the territories on the Europe board count for Europe income, and all of the territories on the Pacific board count for Pacific income.
Italy and Russia both have NOs that talk about warships in the Med. or sz 125 respectively. What exactly is the definition of a warship? Does this include subs or transports?
A warship is any sea unit that has either an attack or defense value, in other words anything but a transport.
If UK Europe falls, can UK Pacific "liberate" any of the territories on the Europe board and then collect that income? I mean if the US liberates a UK Europe territory while London is captured, it gets the income. I would think UK Pacific should be able to 'liberate' and collect UK Europe income too.
No. There is no such thing as "UK Europe units" or "UK Pacific units". They're all just UK units. If they liberate a territory, its control goes back to its original economy, even if its capital is held by the enemy.