Easy out and yes.

Get one of them easy out's
either the kind with a pilot drill on one side and a gripper on the other
or the kind you drill a hole and tap in a bit.
a left handed drill would make even more sense.

could try an old quadrajet d-driver.... can be found practically everywhere... for adjusting gm carbs back in the days of cars having such quaint devices... how'd you get it to break?

i just installed the lancer rejet kit....

I did not notice until after i had done this and got bike back together that the past owner must have also stripped the head off this adjustment screw...

Does anyone have any more info on this..?

so to replace? if i can get it to turn without using a easy out and left handed drill bit ...
do i turn it counter clock wise out until it comes loose?
now by doing this should i be aware of anything like the needle or anything coming out also? and when putting the new one in do i just turn it back in as one would expect clockwise until gently tight and then back out 1-2 turns?

i looked in my manual but must of looked over the idle/mixture screw...?

thanks

thats my carb before i hooked everything back up but you can see the mix screw and how its eat up

The idle mixture screw controls the mixture only at very small amounts of throttle opening.  Is your engine running rich at small throttle openings, mid throttle, or full throttle?  If mid, then you need more height in the jet needle spacer.  If full, then you need a smaller main jet.

If the idle mixture screw isn't yet broken but feels hard or rough to turn, a bit of penetrating oil on the threads and work the screw in-out-in-out until it is all the way out for replacement would probably work.  WD40 is not good penetrant...B'laster PB or Kroil are great, and Liquid Wrench ain't bad.

Any air filter only makes a difference at maximum airflow.  If there is any difference in air flow rates between a clean K&N filter and a clean stock filter, it would only be at full throttle and high rpms.  In any other case, the intake system isn't overloaded, and at less than full throttle, the throttle is doing its job of restricting the air flow, anyway.  (By the way, the tests I've seen show that the K&N restricts air flow more than stock when each has an equal moderate to heavy amount of dirt in them--keep it clean.)  My choice for an air filter?...the $15 stock-type HiFloFiltro available from any non-Suzuki shop.