Sorry I don't have a picture to send you - maybe a verbal description will
help.

The throttle link is the rod with the spring around it - it runs from the
governor arm to the right-hand (closest to the engine) bellcrank on the
carburetor. The governor spring should hold the throttle wide open when the
genset is not running (the tab on the bellcrank will be as far away from the
idle stop screw as it can get). You should be able to move the governor arm
against spring tension to close the throttle (the tab on the bellcrank
touching the tip of the idle stop screw).
The choke link is the rod without the spring around it - it runs from the
choke spring (in the housing on the exhaust pipe) to the left-hand (closest
to the air cleaner) bellcrank on the carburetor, and when cold, should hold
the choke plate almost closed. Note that this bellcrank has two parts - the
tab the link attaches to, and a second piece that is actually connected to
the choke shaft, and has a tab that the throttle bellcrank hits when it
moves to the closed throttle position, with a spring between the two parts.
The effect of this is that the choke can only be fully closed when the
throttle is wide open - when the genset starts to run and comes up to speed,
the governor will close the throttle which will force the choke to open
partway - even though the tab connected to the choke spring may still be
calling for full choke. As the engine warms up, the choke spring will uncoil
and move its end of the link so that it calls for less and less choke.
The brass fitting on the bottom of the float chamber is an electrical fuel
shutoff valve - it prevents fuel going from the float chamber to the main
and idle jets unless it is energized (and it is only energized when the
genset is supposed to be running). This is done to prevent the genset from
'dieseling - running on - pick your term' when shut down.
From your description 'lots of white smoke', it certainly appears to be
flooding - either you have the choke linkage messed up so it can't open the
choke as it starts to fire, or you have a float/needle/seat problem in the
carburetor.

Alan