Best of luck studying for the next little while! I am also studying so I can relate.
The good news is that your brain requires a lot if energy for its metabolic needs so just sitting there studying means you're burning calories. When I have to sit for long periods of time and literally cannot schedule in workouts, I make sure to eat really healthy and drink lots of water. Also, avoid eating while studying. This is a bad habit because for one you're not as aware of how much you're eating, but also because every second spent eating is a second being distracted from learning something. When you study for long periods of time you also build up an appetite and then you can enjoy your meal properly or even some socializing.
Truth is, we can always make time for exercise, even if we live in a big city and all the gyms and yoga studios are a half hour drive away. I find taking walks with my friend/boyfriend/dog in morning or evening is a great way to get many things in one package: fresh air, socialize, and exercise as a great study break. You don't have to be hardcore with exercise during this time because you need lots of rest to solidify all the information you're leaning, but it's really beneficial to get some exercise in every day even if it's mild, to keep that blood flowing and those muscles working.
I'm not sure what you mean about losing weight in your feet. I think you mean swelling around your feet, because this is not usually an area of the body with significant fat deposition in proportion to overall weigh. If you mean swelling, then it's a good idea to get it checked out by your doctor in case it's peripheral fluid retention which can sometimes indicate other health issues that may need attention. If you meant weight loss in your legs, I really recommend yoga and Pilates and cycling! Hope that helps :) study hard!