Guild Wars 2

I mean, if I complete the 50% of the World Map with one characted, and then complete the other 50% of the map with another.
Does that count as the World Completion Achievement?

Doubtful. If I unlock xx% of the world and switch toons, that part of the world isn’t unlocked unless I’ve been there on that toon. I would assume this would also carry over to the chieve.

Each character has its own 100% completion (for the star and Gifts) indicator. At least for me, however, the two gifts I received for my main (my alt is only level 30) were bound to account.

‘Been There, Done That’ must be earned on one character, since it specifically specifies so. ‘Been There, Done That’ requires both 100% map completion from the map elements in the open world, WvW, and Chantry of Secrets; and unlocking all the explorer achievements (Kryta, Ascalon, etc.). Once I earned it using my main, I could use the title on my alt.

You said you could use the title on your alt…does that include the star besides the name as well?

The star, unlike the title, cannot be shared and only shows up on an idividual character with 100% completion.