How much room do they need?
I'd say a 20-gallon minimum. If you want more than one, you'd need a larger set-up (in general, though, I'd recommend sticking with one).
I don't know what you mean by this...you can't exactly play with newts or anything. They shouldn't be handled unless absolutely necessary. That being said, mine ate out of my hands and were docile when they did need to be picked up. Compared to other newts, though, they're rather territorial (which is why I recommended a single newt).
How much work is their upkeep compared to aquatic frogs?
Newts are sensitive to water parameters (even more so than frogs in my experiences) so they require more upkeep to keep their aquarium clean. Since paddletail newts are almost exclusively aquatic (as opposed to say, a firebelly newt that'll go on land), it's imperative that the tank is cycled first and well-maintained. You should have a good filter (but not one strong enough to push them around) and perform weekly water changes. I also kept live plants with mine in order to improve the water quality further.
A good paddletail newt diet would include some live foods, such as blackworms. Make sure you're willing to feed live foods.
Paddletail newts, like most newts, prefer cool water. You need to have a plan for the hot times of the year...moving them into the basement where it's cool, having them in a room with air conditioning, or even buying a chiller (the last option is the most reliable but also the most costly).
By the way, I've seen a few different species labeled as "paddletail newts" so I would get the scientific name of the species you were interested in
. And is there a reason why you want a paddletail newt specifically? I only ask because there are other newt species that are smaller, hardier, captive-bred (many paddletails are wild-caught, although I'm sure there are some captive-bred ones), less territorial (meaning you could have more than one), and overall easier to keep. Look into firebelly newts and Oregon newts