For some of your articles, a different template variation is assigned to their associaated menu item, which uses some different styles for the content. JCE cannot load the styles for this assigned template when you are editing the content in the Joomla admin, only when you are editing the article directly in the front-end.

I don't understand the technical language. I just want to be able to use the editor's basic functions. I'm not doing anything special. I don't understand why I'm having all of these problems. This is frustrating. I should be able to use the basic editing features with no problem.

- Is this a JCE editor issue or did my developer not make my template correctly?

It looks like the person who worked on your site created a variation of your main template, with some different styles assigned to it, and assigned that template to specific menu items, so the articles linked to those menus are displayed using those different styles. Unfortunately, when you use the editor in the Joomla Admin, it can only use the styles from your main template to style the editor content. This is why you are seeing a difference between the content you are editing, and the display of the content in the site, for some pages.

http://prntscr.com/uab8lr
http://prntscr.com/uab9ex - this big gap shouldn't be here.

The gap is added by your template styles, outside of the editor content. It looks like the gap was made larger than the original value used by your template.

Before the person redone my template, everything was working fine. From when I first had my Joomla website, the editor preview and live site showed almost identical formatting, and I never had these formatting issues. For example, how do remove the bold here, http://prntscr.com/uabhzq. The editor shows that it's not bold, but the website is bold. http://prntscr.com/uabjeh

This is the another example of the difference between the main template, and the variation of the main template I described above.

Did he screw up making my template? Why would he make my template this way?

No, it is quite a common techinique to use multiple variations of the same template on one site, as it allows you to easily make some pages or categories look slightly different to the whole site, while keeping the general theme of the site. This is essentially what your developer has done on some of the pages.

So how, and what exactly do I ask my developer to fix so that I use all of the JCE editor features?

This is really just due to a current limitation in the editor, where it is unable to use the styles of template variations when editing content in the admin area of the site. I am loking into this to see if I can fix this issue.