You can use Splunk for Business Analytics. Please refer to http://www.splunk.com/content/dam/splunk2/pdfs/solution-guides/splunk-for-business-analytics.pdf
Splunk allows customer analyze data in move or data in fly in real time where as BI is more suited for static data. Please note Splunk can't replace BI tools. But you can definitely integrate Splunk with BI tools such as Tableu, MicroStrategy etc.
Yes.
Example: Business Objects- where you load the structure/configuration table and drag and drop elements you need. Here in splunk, you have a new feature called Pivot where you pretty much drag and drop fields to create the visualizations.
In BI tools, you create reports,views with simple sql like queries and here in Splunk we use SPL (Search Processing Language). similarities are very close.
Example BI Query = If(This).Do this.Else.Do That|where This != That
Splunk Search: If(This).Do.this.Do That|where This != That
Reference Card: http://dev.splunk.com/web_assets/developers/pdf/splunk_reference.pdf
Documentation: http://docs.splunk.com/Documentation/Splunk
And the best of all: http://answers.splunk.com/
Happy Splunking!
Raghav
In addition to @Raghav2384's awesome suggested readings, if you haven't had the chance to check out Splunk's Search Tutorial, I'd highly recommend doing so to answer some of your questions and concerns:
http://docs.splunk.com/Documentation/Splunk/6.2.2/SearchTutorial/WelcometotheSearchTutorial
PS - Sorry @Raghav2384 if you got a notification about an accepted Answer just now. I clicked it by mistake when I was going to add a comment.