Odo not having the disease is
a continuity error. Since it's said later that he got the disease from Section 31 during season 4, you're right that he should have gotten sick. You could explain it away by saying that something on that planet cured Odo of the disease. Like the writers, I guess no one at DS9 remembered that particular detail and so they never thought to attempt to look for a cure on that planet.
As for Odo's shapeshifting ability, I'm with the side that says just because he has the memories doesn't mean he's able to do it.
Going a step further on the body builder example. Yes, if you had the memories of a body builder, you'd know how to build your muscles and get into excellent shape. But just having the memories alone isn't going to change your body. You'll still need to work at it.
The closest comparison I can think of in Trek is the Trill. Dax has other people's memories but that doesn't make her able to do everything the previous hosts could as well as they did just because she remembers it. She has the memories of a professional gymnast, but we never see any indication that she has any gymnastic abilities. We did see Ezri able to stand on her head against a wall. But that doesn't take a lot of gymnastic ability. -- I just tried it. It wasn't enjoyable, and I don't want to do it again. But I was able to do it, and I never learned gymnastics.
I also don't think she was as good with a Bat'leth as Curzon. Though that's just my take. There's nothing solid I can think of to back that opinion.
I do agree about wanting to see Odo's shapeshifting improve. I thought the same thing even before "Children of Time". It would have been cool if Odo had gradually gotten just a bit better each season to show he was learning.