Yes, you can download it to all your machines. I remember, there was a maximum of 5 installations, but I can't find any verified info on that, so there might be no limit. Personally I did 3 installs without any problems from the Mac App Store.
If you buy directly from Serif, you can use it on all your Macs, too. An exception is, if you're a commercial enterprise. In that case, one license is valid for one Mac. More info on licensing:
https://www.apple.com/legal/macapps/stdeula/ -> a. Scope of License
https://store.serif.com/en-us/help/ -> How many computers can I install a digital product on?
There might be an update to version 2 in the close future, that will need an extra purchase. As there is no upgrade option on the Mac App Store, it could be an advantage to buy directly from Serif's Affinity Store, but nobody knows.
In short:
- Adobe InDesign does have a Data Merge feature to get bulk letter done. That's a feature Affinity Publisher (AP) is missing.
- With InDesign, one can export PDF 1.3 standard. As AP is using a third-party solution (PDFLib) for export, it can just serve PDF 1.4 and higher. E.g. with Adobe Acrobat Pro, one can convert it to 1.3 standard, if needed.
- The nested styles for text design in Adobe InDesign offer much more complex possibilities than the one in AP.
- There is no eBook export, like EPUB in AP, yet.
For me AP is worth its money and the Affinity Suite with all three apps works seamlessly together. Depending on your needs, Affinity Publisher isn't matured as Adobe InDesign, but it gets the work done for most DTP tasks for digital and print. I recommend to buy all three apps.