#1 and #3 are ok casually, but you need to rewrite the dates as they are unclear.
8/3 can be the 8th of March in some English speaking countries (UK English), and the 3rd of August in others (NA English). So you may book the wrong dates depending on what website you visit !
Be more explicit and say, "8th March - 8th August" or "3rd August - 8th August" if that is what you mean.
#2 is incorrect. 'on' has to be used for a specific date, not a range of dates.
#4 is possible .... with a change.
"I want to book the flight during the period 8th March ...etc"