You ask some excellent questions and it sounds like you have a good handle on what you need to do. In theory, those unmatched banking transactions should hold. However, with that being said, if it were me, I would order the switchover exactly as you laid out the questions. First, make the time to match those transactions and then make a backup after doing so.
Since the gap between versions is large, I would update to the latest release within QB Mac 2015 before performing the upgrade. Also, the system requirements do not even mention Yosemite, so you should install to High Sierra, as you already suggested, before performing the new installation.
I remember years ago, the license agreement did allow for installation on a desktop system as well as a laptop, yet, as you install 2019, review the license agreement to ensure that is still the case.
Last, but not least, please remember to backup, backup, backup. It will help mitigate any problems should you encounter them. You want to keep your data intact.
Hope this helps, ~B