Only On-page will be little bit tough. According to Google content is king n links are queen. So, How could an empire possible without queen?

you can't just do your research this way. This is one of the most inaccurate ways of doing seo research that was taught by many 'seo gurus'. You need to do multiple keyword research like who's on the top page, how many links they have, quality of their links etc.

so if there are not many quality backlinks at thew top page of a competitive keyword, its easier to rank for??

No On-page seo is going to rank you in a competitive niche.... You need links, and if your competition has good links then you need good links too.

How you get them is up to you.

Trial and error works better than asking people; google reacts differently every-time.

sure; it's possible if the top sites don't have many backlinks.

It's always a good idea to do the complete SEO to a page in this order:

1) know the product or service you are offering
2) research keywords that are very relevant to that service or offer and select the keywords that have high search capacity and lower competition
3) build relevant links back to that specific page with those keywords selected as the anchor text

Just do the above to each page for the best results in any niche

no, now a days, most important is off page SEO, except title and URL, other on page SEO methods are not very important.

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You have to work on both on-site and off-site SEO to get a good ranking in google.You cant neglect the contribution of backlinks for ranking a site.

From my experience if you want to see your page at the top of the google page then you have to choose 3-5 better keyword obviously it would be your content related. And finally you have to promote that on different site.