What are hybrid SSD/HDD disks (like Seagate Momentus XT) practically? Do PCs recognize them as 2 separate disks (would be pretty convenient if I could really partition them independently and chose what to put on the SSD part) or what?
They're a HDD with a SSD as a cache. Practically speaking, they supplement the small ram cache all drives have with a significantly larger SSD cache and usually don't appear as two devices - for all intents and purposes appear as a single HDD (as opposed to say some form of ram or JBOD with a single volume).
Apparently the latest drives do the SSD caching entirely transparently. Older drives needed a driver. Neither drive seems to allow for independent use of the SSD cache.