Re: difficult stomach fat
While ab exercises will make those muscles stronger, they will not "spot reduce" the fat there. Fat is gained or lost in genetically determined patterns, so you may just have to lose more body fat in general (burn up more calories than you eat).
You may want to consider using body fat percentage as a means of tracking your state, since weight includes both muscle and fat, and exercising can increase muscle (which is healthy, even though it makes you heavier). Note that your current weight is well within the usual "healthy" weight range, though it is still possible to have too much (or too little) body fat.
For weight training, you did not mention doing much in the way of big muscle exercises. Working the bigger muscles may help them grow, increasing your metabolism more to burn more calories even at rest. The bigger muscles include chest (pushups, bench press, dips), back (pullups, rows), and upper legs (squats, lunges, etc.).
As far as eating goes, you did not describe what you eat currently, but you probably know what kinds of foods to eat (vegetables, whole fruit, beans, whole grains, fish, lean meat, skim dairy) and what to avoid (most processed and packaged foods, sugary drinks, foods high in both fat and carbohydrate).