Merging Failure modes: For me “inoperative” and “failed to operate” is the same (description is different because this two can result from 2 different data sources or 2 different persons).

You are correct. *inoperative* and *failed to operate* could be merged. This can be done by simply adding the two percentages of the modes that you believe mean the same.

Non Applicable Failure Modes: If I put all FM (even that which are not applicable)… … is time consuming and useless (for that which are not applicable).

For modes that are not applicable – you could eliminate them, and use only the modes that do apply

Beta (1629A) is not “probability of occurrence” but probability that particular failure mode results in indicated severity classification.

Yes, that is the correct interpretation if you are using MIL-SD-1629A —which means it is the probability of occurrence of the mode at that severity level.

Which failure rate should you use, “summary”, or for specific environment and quality? Sometimes Env. and quality are not so influential and FR (for specific part) for different env. and quality are the same. Am I right?

If the sample size (number of operating hours) is large enough, use the quality and environment. If the number of operating hours is a small value, then the “summary” data may be more useful. I agree that there is not always a direct correlation between quality, environment, and reliability.

Sometimes quality and /or environment could be influential – sometimes they are less influential. The lack of conversion tables does not mean that the failure rates in all environments and for all quality levels are the same – it simply reflects the fact that reliability is a complex function of many variables that cannot be reduced to simple conversion tables.