Well I found out why I couldn't delete certain files and folders. It's because they were locked. How or why they were locked in the first place is beyond me. But at least now I can delete files!
Okay, I'm new to Macs as a home user (I did however use them for video editing at my college). I've only had my new Mac Pro for four days. I have so far successfully managed to transfer all of my PC windows files across to the Mac. I can delete some of these transferred files easily enough off...