Your petcock/carb leaks and the throttle problem all scream of fuel that went bad. Smell the tank (from a distance) It will probably be very rancid.
Some petcocks can be rebuilt, others replaced only. Rebuild the carb and read up on tank cleaning.
I suspect this will be all it needs. Change the trans oil as previously mentioned and look close at the tires for dry-rot. Lube all moving parts.
Read through the wiki especially Freds guide. That bike is well worth saving.