1)Does FDA accepts manual integration of the peaks in the analysis of related substances?
2)Are following comes under manual integration:
-Forced peak;Forced drop line;forward horizontal;reverse horizontal;tangential and exponential skim?

So long as the technique is described in a validated method and is consistently applied, I believe that they will.

Can anybody speak from direct experience on this (i.e., you have run a validated method that uses one of these techniques)?

I am quite of the same opinion, that is when the method is validated the whole of it should be accepted.
We are currently running a validated method for the determination of related substances which can only work with manual integration, given the complexity of the signal. Apart from the main peak, all the other substances are at trace level. I believe that in such cases, accuracy of the measurement should prevail on the automation of the analysis.
However, I would appreciate to know if there is any "official" pronouncement from some regulatory authority about correctness of integration. I only know some papers from literature.

I will never understand how some analytical methods come to be 'validated'.

With very few exceptions validation is entirely dependent on the correct functionality of the data processor, and in many cases this functionality is not merely unproven, many data processing algorithms have been proven to not work. Other algorithms are simply unknown.

Specifically, horizontal baseline projection does not work, nor does valley-valley skim. Other more important features of data processing such as perpendicular and tangent skim separation are so conditional that they must always be used with care. They are not short-cuts through inadequate chromatography.

No information is published by manufacturers about how peaks are actually measured by their data processors. It is tempting to ASSUME that Simpson's Rule is used and that the data sampling frequency is sufficient (20 samples/peak is not enough, 50 samples/peak is a better rule of thumb), but try proving that measured peaks are not under-sampled and you will come to a grinding halt.

Matters are further complicated by the fact that an increasing number of samples/peak are needed, as tailing increases, to achieve the same measurement error (other things being equal).

Perhaps the FDA and other regulatory bodies are putting too much pressure on analysts so that they stop method development once certification of a method is achieved. Why rock the boat with questions of data processor accuracy?