You seem to be chasing your tail!
I've just been through the master cylinder and booster change out and was a bit confused myself, Namba cleared the booster function up for me and I will try too help give you some advice if I can.
first off you haven't said if your car has a Weber or the stock Solex Carb. adjustments differ on the two. Your car sounds to #1 have a vacuum leak via the booster, #2 carb. fast idle cam adjustment is incorrect when it's cold and the choke is engaged. Forget about adjusting the carb. however until the vacuum leaks are sealed. My car has the weber carb. and there is a cam that sets on a screw and comes into play once you depress the pedal, it also doesn't like much gas pedal input when cold. So when I start my 72 GT I get in pump the pedal then take my foot off and turn the key and start her up. I now have my fast idle cam set to around 1500 RPM when it's dead cold and the choke is fully closed, once it has warmed up it idles around 950 in park and about 750 in gear (automatic trans.) As the engine warms up and the choke plate begins to open it will roll off this cam and not come into play via the linkage. The Weber has a cam and screw, the solex has a linkage with an adjustable nut, I would suggest you research carb adjustments for whichever carb you have once you get you vacuum leak fixed.
Now as for your booster, just because it has got brake fluid in it it's not necessarily toast unless the diaphram has got a hole in it. You can clean out the booster housing with brake clean, brake fluid attracts moister and will rust the insides of the booster. The booster has vacuum to the front side where the hose attaches and ambient (outside) air that is drawn into it from the back side when you depress the pedal. If the diaphram was to have a hole you would have a vacuum leak through the booster. I'm somewhat confused at your post #1 you state the brake booster hose going to the carb. This hose should be attached to your intake manifold fitting below the carb!!! with a check valve approx. 6-8" from the manifold connection... The fitting on the carb. (weber or solex) should go to your vacuum advance on your distributor. #2 round spring fitting into the rubber gasket on the booster???? The only spring there is is inside the booster and is a large spring that can't be removed unless you disassemble the booster! ( so I'm unclear what spring you refer to)... #3 there is no way you can check for a vacuum leak by just holding the master cylinder onto the booster with your hand, it has a round o-ring that fits around the base and seals the master to the booster when the two nuts are tightened down!!! So you have to wrench the master down tight to the booster or you'll have a self induced vacuum leak!!! Now as for the hose fitting gasket at the booster OGTS has these, or you could try Kragen in the HELP section where they sell PCV valves and replacement parts like door handles ect...get the master bolted up first then spray this fitting with carb. cleaner WD40 ect... it might not be leaking.
I hope this has shed some light, #1 get the vacuum leaks fixed via your brake system and then look up the adjustment section for your carb. and worry about the idle. Otherwise your just chasing your tail!!!