Unfortunately I really cannot provide support on custom things people do. Plus, if your site is not accessible, pasting code or doing screenshots makes it almost if not impossible to see the source code visually and to see what is happening. For instance, when troubleshooting things like this, using webmaster tools that now come with browsers, you can view the code and actually see where and what is causing the problem. I use the Chrome browser (popular for site development) because when you put your mouse anywhere within a page and right click, then choose Inspect Element, you can see and perform live editing on the spot to find the solution.
My only advice is to use the webmaster tools with your browser (most browsers have this feature) to find out what and where the issue is. Each browser has their own version of webmaster tools, but I find Safari and Chrome to have the better tools. The other option is to add your table in first with no content, test the page, then add a bit more to your table, then test the page. This might help you pinpoint what is creating the extra white space.
Regarding your buttons… delete the space but make sure you do that from the “Text” tab of the editor so you know what you are deleting. Also, please be aware that adding custom code such as you are doing, the WordPress editor is notorious for changing a user’s own code that they enter in…sometimes the changes are not visible. Where you think there are no extra blank lines, it puts in blank lines. You may want to consider using a more advanced editor plugin that lets you see “all HTML” tags. I had to do that with my demo sites by using the Advanced TinyMCE editor because the WP one was putting in extra empty