Changing the pitch for multiple parts of my recording

This is an organisational thing, and yes you have to discover how Multitrack works, because it's the answer to your problem. Firstly though, no - you can't make multiple selections in Waveform view. We'll just get that one out of the way now - that's never been an option.

Fortunately you don't have to be able to record in Multitrack to do this - all you need to do is record a part at a time ideally, but even that's not absolutely necessary either. If we take the case where you've recorded a track in Waveform view and there are different characters mixed up in the same file, then what you have to do is put marker ranges around each part of the file that you need to treat separately. Just make the appropriate selection and hit F8 - this will create a marker range in the markers list. Do this for all of the sections you want to handle the same way. Also, you can give each marker a name, which makes it a lot easier to keep track of them. Now, if you right-click on any of the markers in the list, you will be given the option to insert just that marker's worth into a track in Multitrack, in the session that you will have already started (hint...). What should happen is that it will insert it at the point the cursor is on whichever track is highlighted.

Despite what you may think, the replay quality in Multitrack is identical to Waveform view, although it may be 3dB quieter, because of the pan law settings. Don't worry about that at present - it really isn't an issue. Anyway, when everything you want to pitch-shift for any one character is in the track that you are now designating to that character, you can apply a replay pitch-shift to it. This won't affect the original file at all - Multitrack is non-linear (everything's virtual). Your final mixed-down result gets exported, and that's where you hear all the effects you've applied. What you should end up with is a track for each character, and then you have other options too - you can position them easily in the stereo field, and indeed do almost anything you like to them. Even better, none of it's permanent so you can change things and do another mixdown without loss. It's altogether a better way of working, and fundamentally the way Audition was designed to be used.

If you can't record in Multitrack, it may well be that you haven't set the track input to the correct source. That's very likely to be the case if you can record okay in Waveform view. Here's a clue:

The sources on your machine will be different, but that's what you are looking for.

Multitrack is the only way to go

In multitrack put all the parts for character A on one track and all the parts of character B on another etc

Then you can use manual pitch correction on each track seperately