If I get more backlinks, will I have better SERP in my favor? As in, all my keywords will be closer to the top?
The relevance of the linking page as well as the anchor text in the link has a lot to do with ranking in the SERPs. As a result, each link helps that one page and term a lot. Each link also strengthens your overall site so it helps the other SERPs a little.
As the poster said above, the site linking to yours should be relevant and contain the proper anchor text, usually the anchor text in the "contexual" link should be the exact keyword or keyword phrase your trying to rank for. Remember, with links it's "quality" over quantity.
Yes. Ofcourse.. the more incoming links you get the better your search engine rankings.. and the relevancy of those sites also plays a major role.
Only back links are not enough to boost your site over SERP.You must do relevant linking including keywords with your anchor text.
If you have solid OnPage SEO done, by adding more links with the proper anchor text in the link, you will start to rank higher. As the link count goes up, so will your SERP ranking. Just remember the relevancy of the site is really important.
If you want to enhance your backlinks then start doing off page optimization and if your backlinks increases automatically SERP will be better.