In Go database/sql package it says it is rare to close the database with db.Close because it is meant to be shared by many go routines. Then which one is better when we are given 100 functions that queries from a same data:
1 is easier because if one fails other 99 can still be working. And no need to pass database connection arguments. But in performance wise which one is better?
You missed an important part of what the documentation says:
The returned DB is safe for concurrent use by multiple goroutines and maintains its own pool of idle connections. Thus, the Open function should be called just once. It is rarely necessary to close a DB.
(emphasis mine)
So, your option #2 doesn't actually make sense. The connections are pooled - so use the same connection for every 100 function doesn't apply. Also, option #1 is a waste of time - just do it once as the documentation states, but call Ping after you do just to make sure everything is fine (and have it actually attempt to connect to the database - regardless of driver).