Never heard of anyone signing across the page! Sounds rather extravagant to me. Let's face it, if it's your logbook with your name in the front and your hand written entries, do you really need to convince yourself even more that it is yours by signing it on every page?
As for the PIC bit, I was always told to put SELF.
Wouldn't worry too much about it really. I write all sorts of things in the Comments section so I can look back after several years now and remember each flight really clearly. Each time I get it signed off on my biannual I think the CFI has a good read!!