Apologies for what is probably a silly question for the more technically literate … but:
I have a Haiku partition on my PC, and I can connect to the internet from that. Can I download Alpha 4 from within this Haiku partition and install it from there as well?
You need to download anyboot A4 image and mount it. Then you’ll need too rename /boot/system to something else, and then copy the new /boot/system folder to the boot volume. Of course, you won’t be able to start new applications while there is no /system - copying with Tracker works just fine, though.
To mount the anyboot image you have to open the Terminal and type
diskimage register haiku-r1alpha4-anyboot.image
After that you will be able to mount the registered image via Desktop context menu.
Then copy the system folder as suggested by Diver.