Hi Root44,
I have divided your question on multiple section. Please find the below details & let me know if you have any question.
a)How big search engines like Google, Bing manages their traffic?
ANS: Search engines have three major functions: crawling & building an index, Algorithms and Fighting Spam. It’s providing search users with a ranked list of the websites they've determined are the most relevant.
b) Do they have like number of data centers in different countries so as to handle the huge traffic of whole world?
ANS: Might be but not necessary. User usually request to application URL & DNS will take call & routed connection based on the Geographic IP, Country, Topology, etc.
c)Suppose I am from Mexico so does it mean that they must be having load balancers in my country?
ANS: Might be but not necessary. There is no option to find customer LB device location.
d) I just want to know how they are doing?
ANS: Please go through below link