Chinese VPS: Since KMT and CCP share home country territories, does either faction holding on to territory subtract VPs from the other? Does this effectively mean that China VPs for either faction if all or nothing and is that intentional.
Yes, they are part of different alliances.
“An Attack on China” in order for the warlords to align, China (Warlord or KMT or CCP) need to be attacked. Does this mean that if the KMT goes to war with Japan, Japan cant counterattack without causing the warlords to align?
Any Japanese attack against KMT, CCP or Warlords will cause the Warlords to Align (Rule 4.9).
Can either Chinese faction Lend Lease? When they are a major power?
Only Major Powers may lend-lease (0.9 Glossary). KMT or CCP becomes a Major Power once its land zone IPP values add up to 13 IPP.
Can a Fighter participate in intercepting a bomber and a battle defending a territory in a single turn
No, you have to decide what it does and declare your interceptors (Table 9-9).
When do aircraft count as being “On a carrier” when it comes to auto MAP and the optional Carrier planes retreat rule.
Planes in a sea zone with a carrier are on the carrier and may also be considered to be on MAP. Planes in a sea zone with no carrier can only remain there on MAP
Can a fighter scramble to defend: the strategic bombing of a facility with AA, the strategic bombing of a facility without AA (railway), an unescorted convoy line, an escorted convoy line, an AWS convoy line?
Scramble to defend all facilites, yes (see Errata). Convoy lines no, only aircraft on MAP may participate (Table 9-7).
Can you lend lease to nation yours is at war with (if all other conditions are met)?
Why would you want to do that?
Can Russia game its income by declaring war on Germany as soon as possible, and then declaring war on every single neutral around its home country to force them to become German owned and get like 8d12 income in July 1939
No, as the increase you are referring to is peacetime income (USSR NRS v. 3.3). At war before full wartime income, it will only get the Sleeping Bear roll.