Yes, openSUSE 13.2 supports UEFI. And it also supports secure-boot.
If you had secure-boot enabled on your computer, then you would not have been able to boot the installer if it did not supports secure-boot.
Most likely you have run into a limitation in your UEFI firmware (or BIOS). Some systems will boot any UEFI system as long as it is Windows. Most are less restrictive.
You should tell us something about the manufacturer or brand name of your computer, and other information such as model number. Maybe someone will recognize it and be familiar with the limitations of its UEFI support.
So the boot manager only lists Windows 10 and I can’t boot Linux.
Which boot manager is that?
On my UEFI boxes, I can hit F12 during boot, and the firmware (or BIOS) provides a boot menu. Is that what you are calling a boot manager?
I now have disabled secure boot and tried booting from the installation-DVD in update mode but I do not know how to proceed from the shell prompt of the temporaty RAM-installation. Can any one please tell me in detail what I have to do?
After booting the install DVD, get to a command prompt. If you are in the graphic installer interface, then CTRL-ALT-F2 will get you a command prompt.
Then run the command:
efibootmgr -v
and post the output here. Either write it down to post later, or redirect the output of the command to a file on a USB flash drive so that you can copy it at a later time for posting. That output will give us some idea about the status of your 13.2 installation.
You would be better off trying opensuse Leap 42.3, which is still currently supported. However, you might run into the same problems, particularly if they are due to BIOS limitations.