Your organization question is barking up the subjective tree. I'm not sure what you prefer.

Yes, you can use [CATEGORY SEARCH] to find your favorites. There's a way to mark Performances as your "Favorite" ones and also a way for [CATEGORY SEARCH] to only list favorites. Or you could place your initials in all of your favorite custom [STORE]'d user/library Performances like "PHL" and search for "PHL". Or you could create live sets and scroll through pages 16 Performances at a time. This is what I do. I don't use [CATEGORY SEARCH] unless to find new content I haven't assembled yet in a Live Set or otherwise just want to try a "1 off" task. You could write down all of the MSB/LSB/PC information for all of your favorites and leverage an external program to organize these Performances. Soundmondo on iOS is one way. There are other software solutions for this. I don't use Cubase in this manner so I'm not sure if that's a good fit or not for the goal of organizing Performances.

Where do performances go after I save them?

Given a recent discussion about the distinction in "save" vs "store" - we may get into a similar bit of semantic ironing here. Your first level of committing Performances to memory that isn't erased after powering down the keyboard is to press the [STORE] button. When you [STORE] - you take what's in the edit buffer (which is not kept when you power down) and write the contents into non-volatile memory. Meaning it'll stick around when you power down the keyboard. Pressing [STORE] for Performances always stores your Performance to the User bank. [CATEGORY SEARCH] has a way to filter by only the User bank. In fact, if you press [CATEGORY SEARCH] more than once - you'll see the filter change to "User" among other filters (all, preset, and your library slot(s)). Or you could touch the "Bank" and set it to "User" manually. This will only list the Performances you [STORE]'d along with the Performances, if any, you loaded directly or imported into the User bank.

When you say "save" - the previous semantic discussion would say that correct use of that term would mean to "save" is the act of writing a file to an external USB flash drive. Performances that are "saved" would therefore be the act of creating a Library FILE (.X7L for Montage) or User FILE (.X7U for Montage) or complete backup (.X7A for Montage). This would involve going to the [UTILITY] menu, selecting "Contents" -> "Store/Save" then selecting the type of file you want to save under "Content Type" and selecting the folder under "Devices". You're going to need a USB stick plugged into the "USB TO DEVICE" connector on the back of Montage for saving these files.

The files never go into random places. There is some burden on the user to learn how the file system works (the fundamentals) in order to know where to look and how to use the tools available. There has never been a philosophy of hand holding with the Yamaha synths I've owned which tends to make the process a bit overly complicated.

I don't need JM Tools. I don't know if you need them or not. You'll see lots of users seeing the tools as a missing link for one or another use. However, I'm not sure you're able to identify yet what's a "missing link" for you and if JM Tools would serve you or not. I do not see you yet know what's there on-board. I would, therefore, advise learning the system a bit more before investing much into external tools to try to solve what may just be a learning curve.