Export Files Size is Always Gigantic

You have access to wide array of formats and codecs for encoding your video, and in the case of H264, you have control of the bitrate. That has nothing to do with a Premiere version. You can set the bitrate, which in turn gives you the file size depending on the duration.

File Size = Bitrate * Time.

As for experiencing slowness while editing that can be for many reasons, but you haven't listed any details about your setup. What is your hardware? What kind of media are you working with? What are you doing in the timeline? Effects? Color grading?

So, as I've said, I've updated, I've cleared the space on my hard drive, and I've deleted the media cache in Premiere. Still slow. Still ginormous files! 

Lower the Bitrate in the Export Settings dialog when you export. (High bitrate=Larger files. Low Bitrate=Smaller files.)