Is the story with the magic items heading somewhere?
During EA? No, not really, he will just like you more.
In full release it will most likely be part of his personal quest / way to romance him.
I mean, yes, it's a mess, but when I can offer him items even after he told me, this issue is settled and the story continues, it would be bareable.
Well, yes the story continue ...
It continue no matter how many other triggers you miss ... and basicaly all you miss in the end are opourtunities to gain additional influence over him.
Its quite possible tho that in final release there will be points in his story when the amount of reputation with him will determine if he leaves us, or stay with our party ... so in that scenario, missing some gain will hurt a lot more. :-/
Are the two stories of the items on the one hand and magic-Mystra on the other to different, independend ones?
Nope.
They are more like two independend entry points to the same one.
Gale (aswell as any other companion) will open to you as you travel together, if you do things he likes ... the death scene, only offers additional possible entry, and chance to gain some bonus points.

And did I get it right that I have to fear to miss stories of the other characters without even noticing?
Yes, this is constant threat across ... well, everything in the game.
Some things are even mutualy exclusive.