Anecdotally, I had a site which was eventually displayed on the first-page search results on Google (no, I will not discuss search rank here) PR7 for the best page on the site which happened to be deep, nowhere near the homepage. Previously the site was on the second page. I do not recall the specific search volumes for the keywords, but they were global registered trademarks and the owner's legal department strictly enforced their ownership (I was licenced). The difference between second and first page was about 0 clicks second page and about 30 clicks per month first page.
After a content update, Google placed my site in the first position on the first page for a particular keyword set (woot!). This increased traffic about 300% over just being front page (but, about 80%-95% of the additional traffic was SEO tools and scraper bots). The algorithm did its work and evaluated. Because I was not the key source company, people clicked back and made another choice after a quick scan of the page, not quite zero seconds but, apart from bots, a higher bounce rate. I eventually settled into a comfortable third position after some time, after initially sliding back to fifth, - which means that I can tell you even the first position offers barely any actual benefit, at least in my example, over being last on the first page. But, I made more sales in third position than I had in eighth to tenth.
Use a good SEO and site evaluation tool to discover how well your pages show up in the search engines for particular keywords. WebCEO used to be alright for a few things but, it has changed and I have not tested it since before then.
Backlinks are certainly organic in normal cases. Obviously purchased backlinks are not organic but (you hope!) that they appear so. Open a forum for your topic somewhere decent and make a simple signature linking to your site and help people with their issues. Not sure your topic, for example, Wilders Security Forum used to be extremely reputable and well indexed for security related topics (mostly security software support). That builds organic backlinks.
Also, instead of buying backlinks, pay bloggers to blog about the topic your site is about and show how your product/resource/information/whatever solves their problem/answers their question/etc. and link to relevant parts of your site or provide citations/referenced quotes.
Average position 19.6 tells me that you are mostly on the second (or later) page so actually, your clicks look okay to me. Try to reduce your bounce rate through any valid, ethical means to capture your audience once they reach your page, be relevant (at a minimum keep one topic to a page but, there is a longer answer requiring a separate post), and you will probably climb up the search rankings for your keywords.
Possibly in April you were on the first page for a while.
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