I don't really know what ACCA will or won't let you do but I expect you wouldn't be able to mention ACCA at all until you are a full member (no longer a student).
As for bookkeeping qualifications, not really something you should need but if you do want this I'd look at AAT, ICB or IAB.
With rates, it depends on a few things really. Location can make some difference for example those in London would charge more towards the higher end. Also the work you actually do and the experience you have. £15-20 does sound about right though... you might be looking towards the lower end just to get going, especially if you don't have much in the way of references or experience. I sometimes charge more, but I do offer an out of hours collection and drop off service as many are tradesmen and have home offices which they're not at during the day.
Be careful with fixed charges, unless you really know the business. I'd say if you do it, quote on a business by business basis and not just on company size and number of employees. Different types of businesses can mean a huge change in work required. I've seen companies that turn over under £100K but need a day a week, and I've seen a company in the millions that only needed a day a month.
A good bookkeeper should be able to reduce the workload of an accountant at the year end. It depends though on the accountant and the arrangement the client has so you wouldn't be able to guarantee it. You would probably need the client to speak with the accountant, or possibly even offer to speak on their behalf to see what the accountant would require for a fee reduction (still to be as profitable for them, so long as you're not taking the bookkeeping work from them!).
I'd think you'll attract clients not just for possibly saving money, but for giving them some real peace of mind that their books are in order. Maybe also the financial information you can then give them. I usually show sample reports of management accounts I can provide them with, along with an info sheet that explains this service.