2) Is it mandatory to run utlu112i.sql script?
Better you should use this it will give you the all the diag info. rather you collect manually using different type of Query like timezone info,audit,archive etc..
3) When should i use DBUA method and when should i use manual method?
Yes, this run give you the information about the Parameters need to update,Obsolete/Deprecated Parameters,DB Components and and its Status etc
you can use any method for upgrade DBUA or Manual. DBUA guides you through the whole upgrade process, including all the steps in the manual upgrade process. if possible use DBUA