Have 2007 suzuki vinson quadrunner 500 4x4,only runs at idle with choke on ,has been sitting for year,new gas in it now.

How long does it run before you get bubbles? Sounds like the line is too close to something hot enough to boil the fuel, what mechanics call "vapor lock" Reroute the line or insulate it.

Take the bike to a PROFESSIONAL...this is too good a bike for a amateur to "play mechanic" on!!

were you just going thru water, when the smoke came or was it steam and you flooded out the gas perhaps, is it liquid or air cooled give some details please.

This is a download. See if it is what you are looking for. 2005 Suzuki Vinson Service Manual

If you left it parked for a year with gas containing any ethanol at all then I would check things like your fuel filter because it might be plugged as well. Ethanol blended fuel is a curse if you leave it dormant for a long period of time.

Have your carburetor cleaned

Air Fuel mixture needs set, and Idle

The sticky stuff is normal. On a lot of dirt bikes and 4 wheelers they have air filters that you are to wash either with a filter cleaner or gas and then you spray them down with a light oil and then wring them out until they have no extra oil in them and the oil helps filter the dirt out of the air heading into the engine. It does look in your picture like it is needing a cleaning.

back firing is caused by un burned fuel passing through the system and not being burned in the cylinder correctly , many things cause this, incorrect timing, is the biggest cause, however since you have a toy,, according to the header in the question, a New RAy Suzuki Vinson 500 1:12 scale, is a toy, that has no motor that actually works, If the header is wrong and you need info on a REAL quad,, reply to this message and I'll assist you