My MacBook Pro's battery has died. Capacity is down in the 2000s and cycles are at about 250. To compound the problem my MagSafe charger has decided to start burning through the cable near the bit that actually connects to the computer. I've been looking around and found replacement batteries and chargers for half price or less than the Apple store. They all say they are genuine Apple products, but should I trust them? If they are imports (I'm UK based) say from Asia will they a) work at all or b) damage my machine? Would I be better off swallowing Apple's inflated prices for peace of mind?
It depends on the sellers.
If you check Amazon or Ebay, they both have ways of measuring reliability and you can always see the comments that others leave. With Ebay, you also have the additional benefit of PayPal, so if it is faulty, you could raise a dispute. I know people who have bought lots of electronic goods, laptops, harddrives, replacement parts from Ebay, and they have all (so far) worked and not damaged anything.
With other websites, you can try googling the website address and see if there are any other websites that comment on their reliability, but to answer your question, you won't know until you try. Maybe try WOT or you could post on forums and ask for input as well and see if anybody has had any experience with the website in question.
To be completely safe, it would be advisable to go to a genuine apple store or use their website.