{jagh vIjonchoHpu'}:

I've have begun to capture the enemy. The event which has been completed, is "my beginning the enemy's capture". But this sentence, does not specify whether "the capturing" is completed.

Theoretically, it could mean as well "I begin that I have captured. the enemy", but this translation, makes no sense.

You have it exactly right. The beginning of the capturing is a completed event. Now you're onto the stage that could no longer be called beginning.

{HoDvaD jagh vIjonchoHmoHpu'}:

I've caused the captain to begin to capture the enemy. The event which has been completed, is the "my causing of the captain". The sentence does not specify, whether the "capturing is completed".

Theoretically, it could mean too "I cause that the captain has begun to capture the enemy", but again this makes no sense.

Correct. I'll bet Klingon time travel involves a lot of those nonsense combinations starting to make sense.

Suppose I write:

{reH jIQuchpu'}
always I've been happy

..with the intention of meaning something like "In the past, I'always been happy to (whatever)".

Does it make any sense ? The only way I can understand it is, "I've been happy, that happiness is over, and this always has happened".

Would you understand this sentence differently ?

When one says I've always been happy, one generally means that happiness has always been one's state up to this point, and says nothing about whether happiness will continue. That would be reH jIQuch with no completion aspect. It's not describing something that's completed; it's describing something that occurred in the past without regard to its completion, and that would be tense. But the sentence reH jIQuch doesn't place the sentiment in any time context, so it's just as likely to mean I am always happy or I will always be happy as it does I have always been happy. Or it could mean all of those things at once. To get the meaning you want, you must add an explicit time context. pa'logh reH jIQuch In the past I was always happy.

If you include the perfective suffix, it means something like you're looking back at the whole experience of being happy, including its ending. I don't think the reH on such a sentence would be very useful. Maybe it emphasizes how complete the happiness was over a long time, that there were no breaks in the overall happiness. This might contrast it with motlh jIQuchpu' I was usually happy; that happiness is completed.

Again, I think perfective on quality verbs can be tricky and not very useful, so I wouldn't hold up my attempts at discerning a meaning as definitive.

-- 
SuStel
http://trimboli.name