Is my baby pre-disposed to obesity?

Perhaps. A recent iom recommendation states: healthcare professionals should consider 1) children’s attained weight-for-length or BMI ≥ 85th percentile, 2) children’s rate of weight gain, and 3) parental weight status as risk factors in assessing which young children are at highest risk of later obesity and its adverse consequences. So, see your pediatrician for health supervision visits and ask each time.
Possibly. There are some things that will predispose your baby to obesity, such as a strong family history of obesity or genetic syndromes, but there are plenty of other things to protect your baby from obesity, like breast-feeding, healthy sleep habits, and eating together as a family. Nurture trumps nature 9 times out of 10 with respect to obesity, though, so don't worry too much.
Possibly. Obesity, like many conditions can be cause by a variety and combination of factors. Common causes are too much activity and/or too little physical activity. But there is also some genetic predisposition in at least some people, however at this time there is no definitive testing.
Depends. Breast fed babies are less likely to be obese than babies who receive early introduction of solids. It has been shown that early introduction of solid foods can be associated with obesity in children.