Indeed the lack of tense can be a bit confusing sometimes and it's taking me a bit of time getting used to.

I'm still working to figure out also how it works with the verb suffixes.

For example, in the 4 possible sentences below, do I get the exact nuances right?

jIvutpu’ ’e’ vIparHa’ 

- I like that I cooked (at some point in the past)

- I like that I have cooked (just now)

- I like finishing to cook (maybe implying that this is when I can finally eat ;)

"At some point in the past" implies past tense, which we know Klingon doesn't have. Instead, the -pu' tells us that "I cook" is a completed action. In English we can't separate tense and aspect, so the distinction is difficult for English-speakers to grasp.

jIvutpu'
I cooked; I have cooked; I will have cooked
I perform, performed, or will perform an act of cooking, and I now, did, or will complete that act.

The single word in no way tells you whether the action is past, present, or future. It means all of them and none of them at the same time, the same way that blue means sky-blue and navy-blue and TARDIS-blue all at the same time.

wa'Hu' jIvutpu'
yesterday I cooked; yesterday I had cooked

DaH jIvutpu'
right now I have cooked

wa'leS jIvutpu'
tomorrow I will have cooked

Contexts like these are required to determine when the cooking happened.

If you don't use an aspect suffix, you are explicitly talking about an action that is not completed (or continuous) in the moment your are describing.

jIvut
I cook; It's true that I cook things

This also does not specify when an action happened, which requires context:

wa'Hu' jIvut
I cooked yesterday; it's true that I engaged in cooking yesterday

DaH jIvut
I cook now; at other times I may not have cooked, but it's true that I cook now

wa'leS jIvut
I will cook tomorrow; tomorrow I'll do some cooking

You can make a similar comparison with the continuous suffixes.

-- 
SuStel
http://trimboli.name