Got my ATPL a few month ago. Some entries were signed by the Captain, most were not. I got the Chief Pilot to sign that the entries were correct and put his examiners number next to his signature. All went OK.
In Lasors where it says you need 250 hours P1 of which 150 can be PICUS, you may find you do not have 100 hours P1. (depends on your flying background). If you have done an integrated course, all the SPIC that you did (ie different to PICUS) counts as P1. If you have a CPL you have enough P1, so don't worry about that.
Send a photocopy of your licence signing page and medical along with your logbook, the form and the money (cheque or card details) and 10 days later a shiny new ATPL will arrive.
If you have any things you are not sure about, you can always call Flight Crew Licensing who are usually very helpful when you have got through the telephone menu.