Greetings and welcome!

I suspect the cutscene referred to in Ru'Lude Gardens is related to the quest, Shadows of the Departed, which also requires completion of the Chains of Promathia missions (and more). If that hasn't been done yet, that should explain that.

The cutscene with Gilgamesh should have happened when entering Norg. To check if you have that cleared, perhaps talk to Colleraie at (H-9) of Norg, and look for the cutscene for Zilart Missions / Awakening.

I hope this helps!