I can say that Difference Engine No. 2 is definitely possible, theoretically, as there was a successful project to build one from Babbage's designs. I say theoretically as I believe they made use of CAD/CAM to make some of the components, which Babbage obviously didn't have access to. It's doubtless that after his failure to produce either of the Difference Engines, after spending the equivalent of two HMS Victorys of investment funds, you will need a very wealthy benefactor with as much faith in the design as Babbage and Lovelace had, only then can you start worrying about the metallurgy and precision machining of the time being up to the job.
The problem with finding uses for it was that most of the Victorian Great and Good simply couldn't imagine the scale of its potential. Remember, in the 1830's machinery was only just about managing to mechanise the task of pulling along cargo, most people imagined machines as metal horses. Asking them to imagine a machine could think, but not quite the same way as a human, is a tall order. What didn't help was Babbage's loathing of explaining it to people, he knew that explaining it opened his machine to critique and he couldn't take it in stride, he was notoriously thin-skinned. Lovelace was better at explaining it, but she would die in around 1851 so has little time to write/lecture about it unless her cancer is butterflied away. Babbage also used his own notation in designing it, one he hoped would be used by a new generation of engineers taught it in school to advance his work, but he never published a text explaining what his mess of squiggles and lines actually meant, so even today efforts to build the Analytical Engine is frustrated by having to decipher his drawings.
But, once you have it made, and have it run a few programmes to compute numbers (logarithms, trig functions, Bernoulli Numbers, the last being the object of Lovelace's famous programme), then the publicity and demonstration of the Engine in action would help bring potential users out of the woodwork. The military could use it for ballistics calculations and encryption (not extremely useful until wireless telegraph, but I can see punch cards being used to form a 'private key' that is added/subtracted to messages transmitted as number code, i.e. you would need to have an identical set of cards on the other end if you wanted to unscramble the message. Babbage loved encryption, I could see him anticipating this), statisticians of all kinds would want it to compute trends from data they'd collected, like the correlation of crop yields to yearly rainfall for different areas, or population numbers of animals after changes to an environment (there's a reason that climate science and ecology crystallised during the 1970's, they are both fields that are voracious in number-cruching), engineering and chemical firms often have to deal with heavy functions and equations that demand absolutely perfect calculation, better to trust an Engine to crack it overnight than to get narcoleptic students to produce the tables, and as it has been said finance and the government would be interested in advances in record-keeping (remember, Babbage designed that thing to have 1000 50-digit numbers stored in, well, 'The Store', and he knew it would be trivial to make it larger), and tax-collection.
As for its speed, he predicted his design could add two numbers together a second. Multiplying them will take a minute. That's 5000 times slower than ENIAC, but it's still one addition a second, every second, with no mistakes until it either runs out of cards or suffers a jam. And those numbers will be, again, 50 digits long at most. No clerk or mathematician could ever compete with that.
The big debate would be on whether to keep using decimal notation or switch to binary when it comes along. A binary computer needs about three times the number of components as an equivalent decimal computer, but those components will be much simpler and less prone to error individually. Not to mention that decimal simply isn't as good on thermionic valves as it could be in gears, so you run into a ceiling on what you can use to represent the numbers.