"To be very honest I couldn't understand core purpose of steemit, is it just another Social Website or is it an earning platform.?"

It is both a social media platform and one you can make steem on.

"How can we use Upvote function and for whom, how does Upvote make an impact on the Author post.?

Up votes in my opinion are an investment of curation to the authors post and also increases the up voters reputation. The impact is a increase in the curation value of the post and the reputation value of the up voter. It means more value for the author and more value for the up voter.

How does vote power increase, what happened if one has low Vote Power.?

I don't know sorry. I speculate that as your vote power increases others value your up votes more.

"What is the impact of Steem Power on Voting Power.?"
Don't know for sure, but think it increases the amount of investment of curation for the post you up vote and or the curation of your flag.

"How does other Vote make and Impact on our Post.?"
It increases the curation value for the post and increases the reputation of the voter.

"What is the impact of Reputation on Steem Power and Voting power?"

Don't know perhaps you would benefit by following a witness @dragosroua whom you could ask these questions. Not only would he know, but he has shown me he will answer if you post questions on his post.