Overheating, rough 1450

[grandpas1450]

Hi all, I've been looking at the forums here and I'm really excited about the community of folks who appreciate these old lawn tractors. I'll give two versions of my first question, the short one and the long one.

The cub cadet 1450 with a 14 horse Kohler and a Walbro carb is running rough and overheating (at least I think overheating, spit vaporizes off over almost every underhood surface within 5 minutes of starting). The only problem I've found so far is the throttle on the carb seems to jump back and forth as it idles; I can smooth out how it runs A LOT by just holding the throttle in place with a pair of needle nose pliers. I moved the spring on the front bracket down one notch and it made it idle higher and helped a little, but its still jumping while idling. Will rebuilding the carb solve this, or is it actually wear on the body of the carb itself that would cause the throttle to jump while idling?

Long version: I'm taking care of my grandpa with Alzheimer's disease and it would mean the world to him if I got his old mower running. He grew up in the depression and he's always proud to say that he made the right investment the first time on all of his equipment which saved him money in the long run "Its too cheap, I can't afford it!". I think this definitely applies to the Cub Cadet, it probably has as much metal as a small car Its been sitting for nearly 10 years and it amazingly fired up with some fresh gas and a battery. The first time I ran it maybe 15 minutes, it was vibrating and missing pretty hard and I shortly saw heat waves coming off the hood. I got worried it was running way too hot and parked it. Its also VERY loud. After letting it cool down I pulled the plug and it looks a little lean, vaguely grey, but I've certainly seen worse. Could it be the air/fuel mix causing this overheating? Is it really even overheating or am I just worrying too much? I also thought about timing, and I may try to dig around for a multimeter and use that method as I know there isn't a timing light around here.
Another point of concern, it doesn't start as easily as it did the first time, hopefully I didn't fry anything on the test start. Now once it fires I have to pull the choke out, and push it in, back and forth to keep it running for the first 3 or 4 minutes. Is this a familiar symptom?

Thanks so much for the help and advice.

-Jimbo