The last is the wooden form that gives the shape to the shoe. That's the shoe shaped piece of wood you see in film one. 'Lasting up' means to put a leather insole on the bottom of the last and then to stretch the flat leather upper onto the last and fix it down onto the insole. That is the name of the process. When it is all dry, the sole is added and the last withdrawn leaving the finished shoe to fit a person who wears a shoe the same size as the last.
Yes, that’s true of domed rivets Mateusz. These are called rivers because they are only 1.2mm thick and are designed to bend over, trapping the leather underneath. That’s why they were originally made of soft iron. Nails are much thicker so-as to resist bending. If you use 26mm nails you will find that they hurt the last as they make bug holes, and also they are more difficult to bend over.