shifting shuts my car off

I see it has an egr valve. If it's stuck that will cause rough idle too.

But the first thing to try is to set the idle a little higher and adjust the mixture screw to get the idle smooth. After you adjust the mixture screw you may have to back the idle speed down. The mixture screw is the one right below your circle showing the numbers. The carb don't actually look all that dirty from the outside. I know it's whats inside that really counts but usually when you see a carb that clean it means it's been rebuilt. It don't take them long to get gunked up.

I can see the fast idle speed adjustment screw and it does look like it's screwed in alot but I can't tell in any pics where the base idle speed adjustment is cause there's so much cluttered up together. But it's the one that when adjusting it after it's warm raises or lowers the idle speed. It could be as simple as it's just turned too far out.