1) You can increase the volume by using Adjustments/Volume, right-clicking on the clip on the timeline and selecting Audio Gain or adding a Volume audio effect to it. You can compress the audio using the Dynamics audio effect.
2) What kind of noise are you trying to reduce? If you recorded with a cheap microphone, it's going to sound cheap. But the audio effects include a numbe of tools for sweetening the audio including a noise gate. Depends on what you're trying to fix.
3) There are several 1920x1080 output options as well as the option to saved in UltraHD 4K. Depends on what you plan to do with the video once you save it (eg, create a BluRay disc, share online, use in another project, etc.). Look in Publish & Share/Computer/AVCHD, for instance.
4) You can get answers to your questions at this forum as well as on the Community Forum at http://Muvipix.com. Muvipix also offers a free 8-part Basic Training tutorial series as well as dozens of other tutorials. AT Romano (who regular posts to this forum) has a very helpful blog. I have a complete guide available on Amazon (The Muvipix.com Guide to Adobe Premiere Elements 13). And of course the program itself includes Guided Edits and links to many tutorials via eLive.
There is certainly no shortage of help out there. But this program runs very deep -- so ask specific questions and we'll be glad to give you specific answers.
1. Highlight/select narration clip...Adjust Tab/Adjustments Palette/Volume Panel expanded and its Volume slider
or Tools Menu/Audio Mixer.
2. In the Expert workspace, you could explore Audio Effects. See Premiere Elements Effects Reference - Audio.
3. Where are you in Publish+Share? Look for Presets under your choice. Pick the appropriate one. Typically the default presets can be customized under the Advanced Button/Video Tab, Audio Tab, and Multiplexer. More details and we can fine tune the reply.
On the other side of things, make sure that your project settings are correct....they should match the properties of your source media.
4. There is no official place to get answers to your Premiere Elements workflow questions. And, Adobe support for the product is limited. I would suggest that you ask your questions here on the user to user basis which has proven effective. I can prove customized and detailed reply to you in this forum. There are a lot of free troubleshooting resources such as that found here.
I did not see post 1 until I had submitted my post numbered 2.