If it's going really fast, check that it's rendering realtime or not. (It says at the upper right side in red while you play through your video) try a pre-render by pressing enter while your timeline is selected.
Otherwise check your framerate to see that it's either at 24 or 30 depending on what film you were using to capture the footage.
If that doesn't work, right-click your frame or clip in the timeline and check speed/duration to see if that's accurate. You can always change it here to try to make it slower.
The footage only seems to loose quality because it's a pre-render. That's normal! It should be absolutely fine once you export it out. A good setting to set it on is H.264 and scroll down to Youtube HD setting. This should keep it either 720 or 1080p yet give you a really really decent filesize. Make sure to use Adobe Encoder when you export/ batch render files because it'll make the compression a lot easier. It should go through automatically when you go to export it and you just have to press "Start Queue" or something like that for it to render out.
Hope this helps! Sorry if I'm not super clear, I'm more used to Final Cut Pro for Mac, but I have experience with Premiere Pro. Feel free to ask me stuff!
