The collector of a PNP transistor is more negative than its emitter. But then the emitter is more positive than the collector, isn't it?
PNP transistors are used in circuits that have a positive supply but no negative supply. They are also used in circuits that have a negative supply but no positive supply. They are also used in circuits that have a positive supply and a negative supply.
No. If by positive current you mean current into the connection, then they are all negative expect for Ie, and Vbc which is the inverse of Vcb. Vce is also negative. That's for normal operation of the transistor.
Signs are arbitrary, but most people may use conventional current. For instance Ie=Ib+Ic is always valid, BUT you can use convention current or electron current, but not both.