I'm going on 69 and that drill press was made well before I was born. It needs a new belt but they are generic, they go by length, width across the top flat, and whether they are V, flat, ribbed, etc. An industrial supply store would be able to fix you up with a new one. The reason the belt is crossed in a figure 8 direction may be 2 fold. First is to control pulley rotation direction. That was a common way to reverse motor direction back then. It may also be crossed to increase friction of the belt on the pulley to keep it from slipping. In order to tighten the belt you loosen that nut on the head and lift the head up until the belt is tight and then tighten the nut back down to hold the head at that height. That may be a 2 person job. It doesn't look like there is a crank to move it up and down with so one person may need to lift while the other handles the nut. However, there may also be some adjustment at the pulleys. I just can't be sure from those pictures.
There are no bells and whistles there but it should still drill holes and it may have some value as a collectors item.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.