First, disable your CSM! The Compatibility Support Module (CSM; aka "legacy boot support" or a similar term) is designed to let boot loaders written for a BIOS run on an EFI. (Most computers introduced since mid-2011 have EFIs, not BIOSes, even though the term "BIOS" is often mis-applied to EFIs.) When an existing OS boots in EFI mode, enabling the CSM creates additional boot paths that, if followed, create complications. Thus, enabling the CSM is far more likely to create problems than to solve them. You may well be running into such problems. For more on this subject, see my Web page about it.
With the CSM disabled, you should be able to boot the Ubuntu installer in EFI mode. You can double-check that it's in EFI mode by dropping to a shell and looking for a directory called /sys/firmware/efi. If it's present, you've booted in EFI mode; if not, you've booted in BIOS mode.
There is no one "right" answer about how to configure your EFI System Partition(s) (ESP(s)). You can share them across OSes or have one per OS; put them all on one disk or spread them across disks; and so on. My general advice is to use one ESP for all your OSes. Partly this is because the Windows installer (at least through Windows 7; I've not checked with more recent versions) flakes out if it sees multiple ESPs.
The Ubuntu installer should detect your ESP, mount it automatically at /boot/efi, and install the boot loader there. You should not be prompted about where to install the boot loader. It gets more complex if you have multiple ESPs.
If your suspicion that your firmware can read your SSD but not your hard disk is correct, then you should put a Linux /boot partition on the SSD. This partition should be about 500MiB in size and have a mount point of /boot. Ubuntu will store its kernels there. Because the boot loader uses the firmware to read the kernels, they must be on an accessible medium. Once the kernel has taken control, the rest of the OS can go anywhere that the kernel can read.
