Hoping you need your consultant/doctor onside to get a pump - but if they decide there is clinical need for one, your local PCT or whatever they are not CAN NOT refuse you one on the grounds of cost. NICE guidelines rule!
Re carb counting, there's an online DAFNE course that anyone can sign up for, developed by the Bournemouth team who are pro-pump - you can find it here but anyone can sign up and do it. Carbs and Cals also has an iPhone app that's pretty good, I have that but not the book.
Re getting pumps wet - they are all splashproof, but not waterproof. You disconnect it and can leave it unattached for around an hour with no ill effects, after an hour you'd need to make up your lost basal when you reattach it. When it's disconnected, the pump and tubing comes off, and it leaves behind the sticky tape bit and a plastic connector bit that the tube clips back onto. The tubing all needs replacing every 3 days max or you run the risk of infection at the site, you do this yourself (it's fiddly but easy when you get the hang of it, much like injections!).
My pump is a Minimed Veo, there are Animas ones that are waterproof I think, and the Omnipod type one attaches to you with no tubing but I've never seen one in use so not sure how that works (though I know you give insulin via a remote control).