The question you care about most:
Answer: probably not. And even if it might help, it won't help as much as other stuff (i.e. good blog articles or other good content). However, Google's official position is that it likes SSL and will give preference to sites that use it (see 2014 article on SSL from Google blog here)
For a really in depth and well-researched article about SSL certificates and Google ranks, check out this article on from NeilPatel.com: http://neilpatel.com/blog/does-a-ssl-certificate-affect-your-seo-a-data-driven-answer/. Warning, this dude wants your business. Be ready for cute, but pervasive ads and pop-ups.
SSL is a way to add privacy to the conversation between your computer and a website. I know, you probably weren't thinking that it was public. As it turns out, when you type a website address into your web browser (e.g. www.Google.com), you browser goes to a place in cyberspace (in this case Google.com) and makes a request.
Think of your web browser as a little tiny messenger man who moves really, really fast to give you digital stuff like web pages. So, you tell him, "Go get me the web page www.google.com". He dutifully springs to the computers in cyberspace that house "www.google.com" and brings you back a web page that looks like the familiar Google home page. Without SSL, your little tiny messenger man may be intercepted on his way to or from Google, and compelled to tell someone what you or Google were sending messages about. With SSL, if your messenger gets intercepted, his language gets remarkably confusing and the interceptor cannot figure out what he's talking about. In case that wasn't clear enough, here's a video:
<iframe src="https://player.vimeo.com/video/135666049" width="640" height="360" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>
SSL can hurt your SEO too, since it can create duplicate content of your website, thus diluting or otherwise confusing your ranking signals. So, it's not a easy choice.
If you're building a new website, it's not a bad idea to spring a bit of extra cash for SSL. If you have a website already, SSL may not be a bad idea, but if you're looking for something good to do with $69, may very well be better off hiring someone to write a good blog article with the same money.