And a good question, it is.
If actual wind / ambient wind / given W/V is provided, should we use that for both takeoff and landing charts?
You need to process the data in a conservative manner. That is to say, do not be non-conservative.
Gusts, by their nature, are unpredictable. If the mean wind is a headwind, ignore the gust factor for calculations. If gusts don't appear for your operation, you will be conservative. If they do appear, then you will derive a modest advantage for the numbers. If the mean wind is a tailwind, do apply the gust using a similar reasoning but in reverse.
If the wind is current (takeoff or in the near circuit area for landing), use the wind advised. Otherwise, use nil wind on the main runway but, if the forecast wind is a potential crosswind problem, also check the weights on a subsidiary runway, acceptable for the crosswind. The lesser of the two weights so obtained becomes your limiting weight for the operation.
Gust factor:
As above. For considering crosswind limitations, it is appropriate to consider the gust as, by its unpredictable nature, you can't predict if it is likely to bite you or not. Be conservative.
There is no specific tailwind limitation mentioned in the performance limitation box of the P-charts. Should we assume the default max tailwind limit is 5 kt?
You don't need anything in the box. The chart grid for wind (for the exams) doesn't go more than 5 kts T/W so that is your limit. You have no knowledge necessary to do the extrapolation calculations so don't. You don't extrapolate any chart data.
For headwind, am I correct in assuming there is no upper limitation unless stated?
That's a reasonable approach. Generally, if the wind is very strong, turbulence and gust considerations will frighten you sufficiently to stay in the clubhouse before it gets to the point of being really dangerous.
The comments are with a certification/performance engineering hat on. I can't guarantee the examiner's view but I would be surprised if it were to be much different.