Yeah. I think you should definitely change the name only when there are many people who are familiar with your website on first hand. I mean changing the website title is like changing the brand name of a house hold item. That would leave drastic effects on the sales unless when people are well informed. So yeah, that's just my two cents.

I am assuming that you mean the 'Page Title'. The answer is yes!

That title should always include the keywords and phrases that people will enter into the search engine to find you.

Also be sure that you have good META Tag Descriptions.

Yes

I will recommend to use a keyword that you are trying to rank for, Buts do not over use it as well.

I am thinking about changing my website title to be more meaningful to what the site is about. I have a website http://indianfreebies.in/ and the title is Indian Freebies. I want to change it's title to eg: Free Stuff or Free Stuff and Discounts in India. will it have a long term or short term negative effect on how my site home page ranks on search engines?