1) I think "This week opens" implies the Quiz Night is happening for the first time. "Next week will be" definitely works in the context of a facebook event. 2) "in so far as is" sounds correct. 3) "based on" is correct here.

1) On facebook, a group called "Talking Tuesdays" wrote: This week opens Talking Tuesday's QUIZ NIGHT!" and then: "Next week will be BOARD GAME NIGHT at Talking Tuesday".. Do they sound odd? Can you say "This week opens..." and "Next week will be..." Yes, these sound common to me. This week begins Talking Tuesday's Quiz Night sounds better to me, but I do understand it the way it was originally written. Next week we will have Board Game Night sounds better to me, but again, the way it is written is common. 2) Would you use "in so far as is" or "in so far as it is" in this sentence? "In such cases, in so far as is necessary/in so far as it is necessary for the efficient operation of the system, the Management Authority shall establish criteria to ensure the priority handling of requests." I would use in so far as is

3)you should use based on, course Brazil's economy depends on agriculture.