Cainites can project their souls to the near Umbra with Auspex 5. The power description (V20 pg 138-139) even says they would be able to travel further into the spirit worlds, where they could encounter spirits, werewolves or mages. This always spiritually.
I'm pretty sure cainites can travel to the Dark Umbra via Necromancy.
It's the Deep Umbra what's complicated. Kindred usually have little power relating to the spirit world (not counting the dead). The Tremere have a spiritual path, and the Ahrimanes had their own spirit magic (but they had to weaken their kindred nature to access it). Those magic forms are weak, compared to what you can achieve with Necromancy. I don't think there is any power or ritual that allow a kindred to travel the Umbra.
Kuei-jin can travel spiritually or physically to both the Umbra and Dark Umbra (Shadowlands and Underworld) with many methods. And they are as dead and as Avatar-less as Kindred (well, some are less dead, but some are more). Their nature do not suffer in those worlds more than a werewolf's.
I'm not sure if an official source has said something on the matter, but I think, given the above statements, Cainites cannot travel to the Umbra on their own, but if someone puts them there, they will be like any other being. They will have a tough time trying to move around, or to go back, though.
Also note that W:tA cosmology imposed that many spirits reacted poorly to Vampires, so that would be a good reason to stick to material world. I think the text "vampires have very little to do with Umbra" reinforce the idea that they could be there, but they would rather not.
Keep him protected by building enough power among your kind that they will respect your claim on this person. You need to make some political allies among your fellow Kindred, pronto. Many Camarilla Kindred maintain mortal contacts that they want to keep protected. A chief tool for this is "if you mess with this mortal, you are messing with me; and, by extension, anyone in this city I have some sway with." There is often a gentleman's agreement stay away from a human another vampire claims, because it ensures that vampire stays away from your humans. This, however, still presents you with a problem if you are a relatively weak vampire (in the blood and/or politically) claiming a high-value mortal.
It's going to be an uphill battle to hold on to your mortal. You'll need to invest a significant amount of your energy and political strategies towards this goal.
- Find ways you can perform boons for Kindred that can help keep the mortal safe. Ideally some, but not all, of these vampires should be ones who might otherwise try to mess with your mortal.
- Gain gossip and blackmail material where possible.
- If you only care about the mortal on a personal level, and not for his temporal power, you try to lower his profile. Other vampires will care less about him.
- If you want him to keep his power, gently use it. You are investing your energy into this man, and if you don't get some return on that it's unlikely that you can maintain enough power to meet your goals.
- Don't piss anyone off too egregiously! An angry vampire will hurt your mortal to be vindictive to you push things too far.
- Don't spread yourself too thin. This mortal represents a risk. Do you claim a small neighborhood as hunting ground? Have a Herd elsewhere? Other people or places you want to protect? Each addition thing/person is a liability, and a drain on your ability to keep them safe.
- Bluff when it makes sense, and don't when it doesn't. Some of Vampire politics involves a shell game.
- Try not to let on how this person is important to you, if it's personal. If it's too obvious he will be used threatened and used against you by an opportunist. A mortal you claim for "business" such as food or temporal power is normal. A mortal you care for as a lover or kin is a big risk because people know you might do anything for the person.
All of these approaches are things I've done or seen done in actual games.
Good luck, you've got a problem that can make for an excellent plot line!
Best Answer
Yes, they find it pleasurable, and anything with blood is prone to it
If you don't mind, I'm going to cite V20 for my answer:
Page 269, Earning Blood Pool
It only lists for Kindred an extra rule to escape:
If you follow to page 270, there is a table listing the maximum amount of blood points you can attain from a creature, which only has a scant few categories:
Human (only adult vs. child)
Kindred (by generation)
Animal (mostly by size except for rats)
Garou