I have a "Cool Sports" 250 I just bought. It runs great when you give it gas on starting, but it will stall if left idling.

So. here's my questions:
1. Is the idle adjust screw part of the throttle assembly? When it's adjsuted, does it "preload" the throttle as it's adjustment? My throttle has alot of freeplay initially, so i kinda anticipate this might be the issue.

2. When connecting the hose from the fuel tank petcock to the carb, it seems the hose is WAY too small. I really had to stretch it out to get it to fit. Could this potentially be a problem point?

3. Air/Fuel mix screw. I screwed thia all the way in, then bscked it out 1.5 turns. Does this seem sbout right to you guys? I know alot depends on location (Texas Coast), but the basics should be the same. I have tuned a few motorcycles in my day, so I think I'll get it figured out, but would love to have some insight from experienced hands.