I'd use a very sharp Stanley knife to score the scraps of paper as tight to the picture rail as you can get it, then remove them. It's hard to get picture rail (technically dado rail as picture rail sits much higher on the wall to hang pictures off #pedant) off without destroying it as I would expect it to be glued and nailed / screwed.
With regards to the skirting that's pretty normal (if on the large side) and would normally be filled with caulk during decorating.
I'd use a very sharp Stanley knife to score the scraps of paper as tight to the picture rail as you can get it, then remove them. It's hard to get picture rail (technically dado rail as picture rail sits much higher on the wall to hang pictures off #pedant) off without destroying it as I would expect it to be glued and nailed / screwed.
With regards to the skirting that's pretty normal (if on the large side) and would normally be filled with caulk during decorating.