The argonians invaded morrowind and destroyed some cities like Mournhold(Capital). But did they actually conquer them, and are they part of Argonia now? I m confused.

I think they only annexed southernmost Morrowind, which was innitially part of Argonia conquered by Dunmer.

I think Argonian armies retreated after razing most of Morrowind to the ground: their first intent was getting revenge on Dunmers.

If I'm not mistaken, one of the Dunmer in Dragonborn talks about Mournhold being rebuilt.

No.

The Dunmer under House Redoran scraqed together an army and drove those cowardly S'wit lizards back into their fetid swamp.

There is no part of Morrowind that is still under lizard-filth occupation.

Truth to be told, that was only retribution for the past. That they waited for the Dunmer to be knee deep into [censored] before attacking (red mountain et. al) was a bit cowardish, but maybe the Argonians were waiting for a confirmation that the Tribunal was truly gone before attacking.

Don't forget that the Argonians repelled the Daedra invasion by themselves during the Oblivion crisis while, for example, the high and mighty Altmers were unable to defend their people and their precious institutions.

I think they onlt took a portion of southern Morrowind under direct control, but the entire southern region is extremely dangerous due to frequent Argonian raids

Well according to the EEC trading map in skyrim tear is still on the trading list so it's possible that Tear is still under dunmer control since the borders haven't changed and I doubt the EEC would use an outdated map.

Check out this map: http://www.imperial-library.info/content/morrowind-province-concept-official

The Southern bit of Morrowind was an annexed part of Black Marsh. I'm not sure if this is still true in the 4th Era or if the Argonians took back their former land and kept it.

My take is Morrowind is effectively non-existent as a polity. Various cities that are still populated have their jurisdictions, but there isn't a collective whole that has a border.