As a precursor to your morning jog you can do classical Surya Namaskar. You can vary the pace, beginning slowly and gradually increasing. And you can do as many rounds or repetitions that work for you.
I'd like to mention that asana is not dolled out like pharmaceutical medicine. These things follow a holistic healing pathway and work on many elements in order to bring the entire human organism into a more robust balance. As such, no there are no asanas for eyes, per se. The best remedy for these sorts of things is to change the initial destructive behavior. Of course where employment is concerned that is not always easy.
Taking breaks to avoid eye strain is helpful, also varying your focal point (because computing is a very close focal point). There are some Chinese eye exercises as well AND there's the school of Good Sight (or the like) at the Sri Aurobindo ashram in Pondy. You can also use an eye pillow in savasana, viparati karani, and salamba setu bandha sarvangasana on a bolster.
These things above also work for your third question, aside from reducing belly. That comes from three things; sensible eating, consistent exercise, and time.