''Close'' Vs ''near'' | near in time
Whenitsclearthatyourediscussingtimeyoucanuseeitherone.Yoursecondexample,(b),createsaproblem.Meetingsandpartieshaveplacesaswellastimes.Whenweheareither"near"or"close"wethinkofplacefirst,thentimeonlyifplacedoesntmakesenseinthecontext.Youmustsaysomethinglike"Thetimeofthemeetingisnearthetimeoftheparty"or"themeetingisscheduledforaboutthesametimeastheparty"ifyouwantpeopletounderstandthatyoumeanthattheirtimesareneareachother.Bytheway,wewouldsay"BrazilianIndependenceDay"without"the."Articlesarenotus...
When its clear that youre discussing time you can use either one.Your second example, (b), creates a problem. Meetings and parties have places as well as times. When we hear either "near" or "close" we think of place first, then time only if place doesnt make sense in the context. You must say something like "The time of the meeting is near the time of the party" or "the meeting is scheduled for about the same time as the party" if you want people to understand that you mean that their times are near each other.
By the way, we would say "Brazilian Independence Day" without "the." Articles are not used with proper nouns (names of people, things, etc.). Wed say "Im standing near Susan," not "Im standing near the Susan." You might say "the Brazilian independence day" if you have been discussing the independence days of several countries and want to be clear about which one is on September 7th, but that would be rare.