Do you have the total hours of the previous logbook in the next one each time? (if in logbook 1 you have 100 hours, in logbook 2 do you report those 100 hours?)
Yes, hours are hours, you want to keep a running total in the different categories.
I would recommend that after the issuance of the UK JAA CPL that you carry everything over and start a new logbook that has everything.
Not a bad idea, an electronic logbook would be a good idea.
B2N2 is correct, you didnīt need to get a new logbook. I personally chose to get a new logbook as my first one was more for private pilots and I wanted to get one with more categories. The important thing when adding the numbers is keeping in mind the different rules, aka FAA vs JAA. A big one is PIC, so under FAA rules, many instances when you may have logged PIC would not be considered PIC under JAA, and make sure that your logbook and paperwork submitted to the CAA reflects this.