Shindaiwa EB854

You have a Walbro WYK series carburetor. They are are adjustable but considering the age it is more likely a metering diaphragm that has stiffen. You should clean the carburetor in an ultrasonic cleaner and install a K23-WYK repair kit before attempting any adjustments.
 
As far as for the center rotary barrel has the idle mixture and may have an EPA plug in it. And there may be a high speed adjustment.
 
Idle Mixture Adjustment

1. Remove the plastic plug directly above the inner idle needle.
   
2. Using a 2.5 mm wide flathead screwdriver, turn out (CCW) the inner idle needle until the threads disengage.
   
3. Turn inner idle needle clockwise 10-12 turns in very slowly. The idle RPM will increase (lean) until the peak lean idle RPM is obtained. Once this is obtained, turn inner idle needle CCW (rich) until optimum idle is obtained. Please note that carburetors and engine applications will vary therefore the neelde settings may also vary also.
   
4. Adjust the idle speed screw to the correct idle RPM.
   
5. Check idle, progression, and wide open throttle.
   

 
Some WYK carburetors have a high speed needle to adjust the fuel flow to the nozzle, High Speed initial adjustment is 1-1/4 turns CCW from lightly seated. This is the preset mixture and is a little rich. Please set this adjust if available to your equipment max RPM setting. Don't exceed you engine max RPM spec.
 
Also to easily remove the EPA plug on the idle mixture require a special tool. (2.5 mm LH threaded puller or 3 mm version if someone had tied digging out the plug)

The inner needle is in the center of the rotary barrel. It accessed through the top center. The idle speed screw is the one the on the top near the throttle that limits the closure rotation of the rotary barrel.
 
From what you describe a cleaning and repair is best as a replacement Walbro WYK-322 (A02102051) is about $70 us plus shipping. The repair kit is about 8-10 usd plus shipping. As I said a good cleaning and a kit installation may be all you need without any adjustments other than a metering lever height adjustment. This because the levers are seldom right out the package.
 
Here is a link to the Walbro WYK service manual. https://www.walbro.com/wp.../2016/01/WYKseries.pdf
 
You could try one the Chinese clones but are they only fit and not necessary a performance match, Some are not even close to being right. Or even have the correct throttle cable mounting bracket.

It should work as the WYK-323 uses the same repair kit.
 
Your carburetor not listed on the spiral cross reference but but may just have been over looked.
 
https://www.walbro.com/spiraldiaphragm/
 
I have purchase one of the spiral kits here but it was mainly to get the new W-Tool so Haven't install it yet beside it is self defeating here as I am a repair shop and need the repeat business.
 

On the spark arrestor screen it is best for it to be in place as sparks could cause a fire hazard depending on how dry things are but many users operate equipment with them removed.
 
On the carb you did set the metering lever height? Plus you still may have to re-tune the carburetor too.

It is flush with the metering chamber floor. Here is the service manual for the carburetor.
 
https://www.walbro.com/wp-content/uploads/2016/01/WYKseries.pdf
 
As for the spark arrestor it should accessible at the muffler outlet but getting to it depend on the engine cover. But according to the owners manual the cover needs removing.
 
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=2ahUKEwiK2uCr7uTlAhUEOn0KHbXdCiAQFjAGegQIABAC&url=https%3A%2F%2Fwww.shindaiwa-usa.com%2Fgetattachment%2F12f56105-acac-4dc0-b4c4-73f8a74100cf%2FEB854%2520EB854RTes_1112_051114.pdf&usg=AOvVaw1_mKzgdxyt_eEKnJt0qQ2a
 
 

mikesWhat do you do when you retune the carb ?

Fuel mixture adjustments. Your carburetor appears to have both L and H speed mixture adjustments. How to adjust is explained in the SM (service manual).