It's similar to how drive letters work in Windows: the partition you installed it on is C:\ and you can assign any other letter to any other partition.
On Linux, the partition you installed it on is / and you can mount other partitions in any empty directory.
Usually you create an entry in /etc/fstab that tells the system which partition should be mounted where. I'd do that in each distro once you have installed all of them.
If you install your first distro without creating any partitions manually, the installer will probably create an EFI partition. Maybe it wouldn't need to create one on your specific system, but it will probably do it anyway.
You can create dedicated partitions for /home, but unless you know why it makes sense in your specific situation, you shouldn't.
The data partition is just another partition that you can mount somewhere, for example /mnt/storage.
If the installer doesn't automatically create an EFI partition, you can create a small FAT16 or FAT32 partition (a few hundred MB should be enough).
The swap partition is just a swap partition - that is the partition type you select in your partitioning tool.
The storage partition can be any format you want. If you don't need to access it from Windows, just use ext4.
Mount points are similar to drive letters, but more flexible. You can read these Wikipedia articles: https://en.wikipedia.org/wiki/Mount_%28computing%29 https://en.wikipedia.org/wiki/Fstab
The order of the partitions shouldn't matter - usually the EFI partition comes first if there is one at all, but as far as I know that isn't actually required.
~~There are no BIOS partitions - you may be confusing the term with the BIOS partition scheme, but that doesn't matter in this context~~ "BIOS partitions" do exist, but they are irrelevant on modern machines - they are for booting GPT disks on systems that only support MBR disks.
If you need an EFI partition, the first installer will create one. As for the sizes, the recommendation in the other comment makes sense to me (one ≈60 GB partition per distro, one swap partition and one partition for your personal files that uses the remaining space on the disk).
Hibernation is an OS feature, so you can't disable it in the BIOS. You can either disable it in all your distros or simply not use it.
A swap partition doesn't have a filesystem - it has its own partition type and doesn't contain files. The installer might create one automatically or it might not - if it asks how large it should be, a good rule of thumb is to use the same size as your RAM.
If that turns out not to be enough, you can create a swap file on a data partition later and if it's too large, you just wasted a few GB but usually that doesn't matter.
The first installer will install the bootloader automatically.
It will also create a swap partition unless you tell it not to, and all distros will use all swap partitions by default, so you don't need more than one per disk.
If you don't hibernate one distro and then boot another, sharing a swap partition isn't a problem.
There shouldn't be any significant difference between the GRUB versions that come with different distros, so the order in which you install the distros doesn't really matter.
You can't install multiple distros on one partition, so you need at least one partition per distro.
You can only mount one partition at one mount point, but any empty directory on one partition can be a mount point for another partition.
GPT is a partition table and is not used for Linux specifically, but on any computer with UEFI - it defines how to find partitions on a disk, but not how they are formatted.
ext4 is a filesystem - formatting a partition with ext4 means creating data structures that tell the OS where to find files and directories in the partition.