Hey dodos9,
I don't think you are being unrealistic with completing the PPL in 4 months. The aspect you may struggle with is the 7 exams. If you can get most of them out the way before you start then you only have to concentrate on the flying and gaining the hours. You are very lucky to have your parents help pay for you so make sure you stay in their good books
. After your PPL get the night qualification which will be around £900 and then start the hour building. By that time, if all goes well you should be earning enough to fly a couple of times a week if full time or every few weeks being part time, you can't start the commercial route till 18, or it may be 21 I'm not sure! But you will have a year basically to build up the 100 hours! Then it's off to pass the ATPL theory! If you have the dedication there is no reason as to why you are being unrealistic. I don't know much but I do know there are alot of qualified pilots without jobs. But if you are willing to take the risk then Go for it you never know!
Best of luck!
Greg