If you've achieved picture lock in Premiere - you're done editing the video and are now mastering the audio - this is a pretty straightforward procedure.
From the Premiere sequence, choose Edit > Edit in Adobe Audition > Sequence... and allow Premiere to generate an interchange session and open it in Audition. You may want to render a reference video to make it simpler, but this is not a necessary step. What we'll be doing here is not directly editing the clips in the Premiere timeline, but generating new clips for an Audition session, then sending rendered, mastered stems back to Premiere to replace the existing audio.
Once this sequence opens in Audition, select the clips you wish to standardize - these would likely be voice clips only and not music - and right-click one and select Match Clip Volume from this menu. You'll be able to select a target level to which you'd like all selected clips normalized. You may need to follow-up by adjusting the levels or mix depending on your needs, but this should get all the clips at a relative level so you're not making wild adjustments.
When you're satisfied with the mix, choose Multitrack > Export to Premiere Pro... from the menu. You can send back individual tracks or buses rendered as full-duration stems, or the master output rendered to mono, stereo, and/or 5.1 stems. Premiere will import these and allow you to place them on new audio tracks in your sequence. mute the original audio tracks and you should be ready to export your final product.
To attack the hum/hiss, you'll want to try some of the Noise Reduction / Restoration effects. Hiss reduction should make short work of any standard hiss while you may want to try the DeHummer tool to remove electrical hum and related harmonics. You might have good luck using the Noise Reduction tool for these operations as well - find a region of audio that contains JUST the noise or just the hum (or both), select it, and choose Capture Noise Print form the right-click menu. Then open the Noise Reduction effect and preview/adjust until you find the right balance of noise reduction without affecting your actual audio signal and apply.