(1) Playing my first solo game as the Axis. When would the Axis include Italy?
Italy joins the Axis through the diplomacy system. In rarer circumstances it can also join the Western Allies (or even Soviets, though I have never heard of that happening).
Can Neutral countries side with the Axis?
Yes, through the diplomacy system.
Although the Appeasement Treaty is in affect, can England land troops to assist France in their fight?
Or - can England Land troops into a neutral country in CASE they are attacked?
The Pro-faction chit means what exactly? If played on a neutral country do they join your side?
Pro-faction means the minor favors your side. If a Political Success is used on a minor with your pro-faction marker, it will then join your side. In essence, you need two successes to bring a country onto your side.