Haroon.
1) Whether one should apply the safety factor after airborne or not? If yes then how much, 67% or some other figure?
Yes. One should ensure adaquate landing distance. The FAA favour a minimum of 15% but it isn't a regulation, just a recomendation. The NTSB has been rather critical of the FAA in not implementing this as a regulation as they believe it would have prevented at least one over run accident. (ERJ170)
There is much guidance around. The flight safety foundation have a good breifing.
Some manufacturers are now including overspeed data as the unfactored figures require Vref over the threashold but if you have used a wind additive you will most likely be above Vref and therefore require more distance.
If you are landing the aircraft at an un familliar weight or on a sloping or wide or narrow runway you will flare differently than normal.
You will flare differently than the test pilots who did the certification campaing because their job is to bring home the numbers not the passengers.
The amount of additive is currently up to you to decide so if you go off the end it's going to be you explaining.
2) If 67% safety margin is required at dispatch to reduce the probability of an overrun then what is it that stops us not to adhere to our flight plan if the situation is not to Land ASAP. Is there anything explicit that stops from using the safety factor once airborne?
It's again not exactly clear. What is clear is that a simple in flight re-planning will still require the 1.67 or 1.92 factor according to the current EU-OPS. Not sure about FAA wording. Any Emergency or abnormal may be justification to reduce landing safety factor due to increased risk in flight but then your q1 comes in to play as to how much to reduce by.