Question: I basically jog for 30 minutes just after work at about 9:00 pm, before dinner. I sometimes have a full lunch at about 3:00 pm, but most of the time I have some fruit because I reach the office at about 12:00 pm, having had morning breakfast at 10:00 am.

1) Is it safe to jog if I am feeling my stomach is empty? (sometimes to maintain the routine, I have to go there directly) I'd just be drinking half a glass of water.

2) If I am feeling my stomach is empty, is it OK to take 3 bananas as they provide instant energy?

3) Or it is mandatory to eat some light snack and before going for a jog?

Answer: 
I think you're over thinking this.

If you personally feel like you need to have something because you feel lightheaded when you've previously jogged on an empty stomach you should definitely have something to eat prior to exercise.

Likewise if you've felt worse eating before a jog, then don't eat.

Any option you choose won't matter for a 30 minute jog. If you feel okay after your jog eat afterwards.
To be completely honest, not eating before a workout or run is actually best. That way you burn fat directly instead of working through what you just ate. However you'll probably feel tired if you've been fasting for a long time (ie: Workout before breakfast). If you do want to eat before a workout I'd give yourself at least an hour before going at it. Don't want to throw up.