Might help explain why it's using /boot/efi - as the system may be a BIOS / Legacy boot device, which EFI would not be used; it is used, just differently. My mums older Dell laptop is like that, but still uses EFI - just not a separate partition due to BIOS / Legacy boot.
What machine are you using (specs)? Also what year was it produced, that will definitely help pin-down what boot type is being utilized.
For HDD's - sda, sdb, sdc = internal disks | sda = disk 1, sda1 = disk one, partition one | sdb = second disk, sdb1 = second disk, partition one - and etc. EMMc and NVMe are labeled 'mmcblk01' for EMMC, 'nvme0n1' for NVMe.
Also - are you setting manual partitions? If it's a full install, no dual-boot - I'd suggest letting the installer take control for partitions and all; even with dual-booting, I suggest using the installer recommendations. Anything EFI related is suggested to use ~512MB, so that sounds right.
Swap - yes, it's there; I can assure you of that Swap isn't handled by a set partition anymore but, you may still use the partition if you wish. Swap is handled by a
swapfile now, kind of like zram, but not quite. The swapfile, I think, is easier to deal with - especially resizing swap. Before, I would run out of swap space but it was a partition - then, I tried resizing the swap partition and killed my system lol.. So, yes - swap is still used. It may be configured as a partition if you wish. I don't have hibernation options in Zorin - that I'm aware of, I only have suspend. Also running no swap, so that might not be an option for me overall. For hibernation, though - it's normally suggested to have a swap space either matching, or over the size of your physical RAM.
Home - was normally a separate partition, like swap. And killed many systems in the past trying to resize that as well I've learned a lot the hard way hahaha But, 'home' folders are normally in the
/home/user/ format from the root of the drive. Like with Windows and the 'users' folder, it's 'c:\users\user' as Ubuntu is /home/user'. Linux uses the '/' forward slash, vs Windows that uses the '' backslash - just some slight differences.
But, yeah if you're setting manual partitions - first partition: EFI/boot ~512MB, second: swap if needed, or home, up to you for size on either - third: your ext4 or other filesystem type (btrfs, ext4, etc.), and for the rest of the size left; much like C: for Windows, that's your user space..
Do suggest letting the installer make the partitions though - it can get pretty complicated, very fast..
(edit) Forgot one tiny thing - if the machine can't see UEFI boot devices or installers (or doesn't install correctly, i.e. no boot), you could use Unetbootin to make the install USB - that still uses the BIOS / Legacy format. Have had to use that to get installed vs using Rufus or Etcher in the past. Rufus has legacy boot options but, they don't really work out for me haha but are there.