AKradian

TMS, where the concept of LAB comes from, had a second season (with Cygnus Knights instead of Explorers). We might get that at some point.

Change your computer's locale (language) to English.

Each row in the Fairy Bros Golden Giveaway Calendar is a week, which is 9 stamps because Saturday and Sunday (UTC) each give 2 stamps.
The event runs for a total of 12 weeks, and requires 11 weeks' worth of stamps.
So if you did indeed miss 9 stamps, you're still able to get the final reward. But you can't afford to miss any more days.
We have 6 weeks + 2 days (including today) until the end of the event.

Is it a normal AbsoLab staff, or a special one from a Relay event?

Prophetie wrote: »

Players would just start carrying bosses every 30 minutes and leaving seconds before the end asking for a share on drops, mesos or less ToS-friendly compensation.
Wasn't it the reason why it was re-designed to be at entry for the mid/late game bosses?

It is already the case that if the party you entered with clears the boss, it counts as a clear for you too, even if you left the party and the map before they cleared.
That was done because KMS used the technique you describe to carry multiple parties through Chaos Root Abyss and other bosses that allow re-entry on failure.