Yes, if you do it gently and make it a positiveexperience, your bunny will not get so stressed when you pick him up.Just think how it feels to him: little bunny scooped up high into theair, kind of like a hawk might do. Rabbits tend to prefer all four feeton the ground, but in time, I'm sure you can get Ralph to accept yourholding.
He should be held supporting his upper body and bottom, so he doesn't feel like he's floating in air.
Rabbits tend to really like their noses and heads being rubbed,stroking towards their ears. Most rabbits will melt for this, some even"purr" (grind their teeth in contentment)
I don't believe rabbits need to be vaccinated or de-wormed, though I am not positive.
The only disease I can think that a rabbit might pass to humans isringworm, which is a fungal skin infection that will make both of youitch.
Bunnies and dogs do not share any illnesses in common that I have heardof. Bunnies and dogs can and often do get along, but it really dependson the dog. Most dogs will be inclined to see a bunny as a moving chewtoy, so I would never leave a dog unattented with a rabbit.
Rabbits can recognize their names; I have two rabbits, and if I callone, they know which one I am calling. I'm not sure exactly what thememory of a rabbit is like, but they are highly intelligent and canlearn and remember things.
Keeping water in a dish is fine, so long as you keep it filled andclean. Is he an indoor or outdoor rabbit? If he's outdoors, you'll haveto check to see he has plenty of water in the summer, that he doesn'ttip the bowl over, and that it doesn't freeze up in the winter (notthat I know how cold it gets in Australia
)
Is he in a wire bottomed cage? If so, he definately needs a restingarea, to keep his hocks off the wire. A wooden plank often does thetrick, though I'm sure there are other suggestions. Many rabbits tolike to have a "spot" they call their bed, something they can stretchout on or snuggle into, like a towel or sheepskin rug.
Hope all this helps. Feel free to ask more questions, we're all here to help!
~M