Let me preface my breakdown by saying this: connotations are everything. This is difficult as an ELL, since you're less likely to have heard enough context surrounding these words to get a proper feel for them. My answer will largely focus on these connotations, which are inherently highly subjective, so I welcome other answers to support mine.
1) Let's take a memorable photo together.
This one works much better for Scenario 2 than Scenario 1, as I fear it doesn't quite grasp the gravity of the former. If something is memorable, it is simply something which stands out in your memory, but you can have a memorable restaurant, a memorable coworker, and any number of memorable anything. This works for some random tourist you briefly bonded with, but to depart from your homeland for many years?
2) Let's take a memorial photo together.
I wouldn't say this works for either, because if something is done in memorial, it almost always means that the object or event in consideration no longer exists. A memorial statue of a great figure strongly implies that the figure is deceased. A war memorial is only built after the war has ended, or at the very least some time after the event it is commemorating.
3) Let's take a photo together for memory.
Not bad, but a tad awkward to say, and even more so to explain. You wouldn't really be taking the photo for your memory, you would be doing it to create memories, or to make lasting memories, or something to that effect. Saying that you're doing it "for memory" is a bit too vague to have substantial meaning.
4) Let's take a photo as memento.
First off, this would be as a memento, as "memento" is a noun. And then we'd come back to my analysis of the first choice -- this would be most appropriate for Scenario 2, not so much for Scenario 1.
5) Let's take a memento photo.
Memento doesn't fly very well here; while you can frequently get away with using nouns as adjectives in everyday-English, these are two defined nouns with separate meanings, and your fusion of them doesn't clarify which aspects you're taking from each word.
You may notice that I didn't strictly approve any of these for Scenario 1 -- while choices 1 and 3 work better than the others, they all seem rather underwhelming for the grave situation you'd outlined. In all honesty, it is hard to find a word that fits here -- as such, I wouldn't even attempt to do so. Because they would be your cousins approaching you, I would say something along the lines of "one last family photo" -- even though it (hopefully!) isn't really the last photo you'll take with them, it's the last of an era, the last you'll take before your life changes so drastically. It is thus that I find it appropriate.
