If my dad is 5 foot 3 inches, is there any chance I will grow taller than him?

Maybe, likely if... Height is mostly genetically determined, if a child has normal nutrition. A child is likely to grow taller than his or her 5' 3" dad if dad's or mom's relatives are several inches taller than dad, if mom is taller than dad, if dad ended up short due to chronic illness such as cystic fibrosis or due to malnutrition such as being a wartime refugee, or if the child's own siblings are taller than dad.
Yes. It depends on whether you're the daughter or the son, but the genetics of growth are complicated, so there's usually at least some chance. Your mother's height is also important because if she's very small, the likelihood that you will be on the smaller side increases.
Maybe. That depends on a few things like: 1) girl or boy? 2) your present age/stage of puberty, 3) other family member heights, 4) does your dad have a history of any endocrine problems? 5) your overall health and nutrition status.
Depends. We try to predict adult height by doubling one's height at 24 months of age but that is not very accurate. There also is a formula of adding dad's height to mom's height, then add 5 for boys, subtract 5 for girls, divide the final number by 2, which also is only roughly accurate.
Depends. Researchers came up with a general rule for predicting height that I use to decide if a kid is following an expected pattern. For boys; moms height + 5 inches added to dads height & divided by 2 gives expected final height. For girls; dads height less 5 inches added to mom's height and divided by 2 gives final expected girl height. This has exceptions. If you want to be tall, pick tall parents.