Participles and times?

Which tenses can you replace with present or past participles?
I've read that you use the present participle, to say that both things were done at the same time. Is that the same for the past participle?
I remember that one grammar text said, that past/present participles always imitate the same tense from the main clause.
And if you want to say, that something was done before, you have to use the perfect participle:

_At the same time (main and participle/relative clause)_
active: present participle
passive: past participle

_Done before_
active: having + past participle
passive: having been + past participle

So the following example sentences schould be correct, right?
- Having unterstood the problem, I helped him. (I first understood, than I helped)
- Understanding the problem, I'am helping him (I am understanding the problem right now and help him instantly)
- Given an apple, he was very happy (He was very happy right after someone gave him an apple)
- Having looked at the pancakes, I will eat them. (I have looked at them and decide now in the present, that I will eat them)

Are these sentences correct?
Looking at the pancakes, I will eat them
Loving this girl, my jealousy had killed me.

Thank you!
(This is one of the topics, I really have difficulties with!)