and do you need to have tribunal/bloodmoon installed?

You don't and no. You have mistaken the fact that MGE contains an internal version of MWSE for the idea that it requires it. And you don't need tribunal or bloodmoon.

I thought you needed the last Bloodmoon patch or something like that for MGE?

I thought that too.
Even if you don't have the expansions, you need to install the official Bloodmoon patch, to trick MGE into thinking you have v1.6.1820

(if you do have the expansion, be sure to install them. They fix/update the game very well.)

Yeah you do. But (somewhat oddly) you don't need Bloodmoon to install its latest patch.

At least that's what I seem to remember.

You need the Bloodmoon (1.6.1820) or better executable, but you don't necessarily need the data files (ESM/BSA) enables. Some of them must be present (particularly the snowflake mesh), or you'll run into some errors.
Edit: For clarification, MGE doesn't require the BM data. MGE requires the BM executable, which needs that stuff to start up, I think. I may be wrong though.

As stated, you don't need MWSE, as MGE comes with an expanded internal copy. You may disable the internal copy and use another, but you don't have to (you could even disable it and not use it at all).

There's a dedicated http://www.gamesas.com/index.php?/topic/1117223-morrowind-graphics-extender-mge/ with links to useful info and requirements - please post your MGE related questions to that thread going forward, that way we can keep all troubleshooting together in one place and it's easier for others with similar issues to find an answer.

If you have further questions about this particular issue please post in the http://www.gamesas.com/index.php?/topic/1117223-morrowind-graphics-extender-mge/. Thanks!

Ah yes, let's continue this discussion there.