It seems a bit strange to me that all my body except my chest is well defined and muscular. My chest is actually quite flabby. I do some chest exercises - butterfly, pullover, standard press and incline press, but it seems to have made little difference. Am I doing something wrong? Are there methods or exercises that target eliminating excess chest fat and building chest muscle?
I also would like to know ways to strengthen my core.
I can't help you about the Chest exercises but I just want tell you one thing. I use a video called Core Synergistics, by the famous Tony Horton, which gives great results to strengthen my core. It's part of a program called P90X, I wish I can use this program but I have a dislocated shoulder and a torn cartilage in my knee. I only use Core Synergistics, Cardio X, Kenpo X (but not very often) and Shoulders and Arms. That is the best home exercise program I have seen in my life.
You can't target fat loss to any specific area, but if you start a fat loss regimen, you should see the results everywhere. One thing to consider is that if only your pecs have extra flab/fat, you may have a condition known as gynecomastia. It's surprisingly common, but it is a hormonal conition that needs to be diagnosed and treated by a doctor. If diet and exercise just aren't working and that is the only trouble spot, you might want to ask your doc next time you're in.
Keep your body lean, your blood clean and your mind sharp. -Rollins