Wallace,
We hear you and understand the frustrations you can run into while going through some of the various social network hoops.
However, most networks shouldn't really be denying you if you're asking for the basics. Facebook, for instance, has no approval process if you just need user's to authenticate on your site and you can still obtain their email address. If you need more advanced profile data or advanced features, like auto-posting to a Page, yes, you'll need to go through an approval process.. but that shouldn't prevent the basic functionality from working while doing so.
For Twitter, it's not really common to get denied. When you create your Twitter account and ask for access to the APIs, it's some basic questions and you have to link to your site, I believe. When you try, do you get any details as to why you're being denied? Once you get through that, you should be able to setup your app quickly as there's only a few options to set.
Any details you can provide on the above will help us understand and help you get over the hurdles. Unfortunately, we don't control the social networks and their approval processes. They change frequently, but usually aren't insurmountable.
Secondly, Why do the social media buttons popup over the hamburger menu obviously the menu is more critical that the social media.
Our template file for JFBConnect gives the social button a very high z-index value that works with most templates. If you can let us know what page you're having issues with the social buttons on, we should be able to provide you some override CSS that would fix that issue quickly.
Thanks,
Alex