I didn't hear Mera's father was dead, when did she say that?
It was never said that he didn't train Arthur in Justice League. They only talked about him not wanting his mother's trident or being King, so it could be left to interpretation on any history they had as Arthur knew Vulko's name.
I'll give you that one.
They did attempt to explain that away by saying where the mother box is, was just a strong hold. Weak but still attempted.
They also mentioned that Orm talks of war with the surface (but I don't think Arthur even knew Orm existed in Aquaman, so I'll give you that too)
It explains why Arthur was in some Norwegian mountain town in JL but in a shore town in Aquaman
It explains a little that Mera and Vulko had been trying to convince Arthur to become King for a while as he spoke to them with familiarity. I found it weird in Aquaman that he spoke like he really knew her when in the Whedon cut, he barely spoke to her, and Vulko wasn't in it.