Can you tell the amount of electrical service entering the house by the wire size? If so what is this ones?

Can someone give a description of what's wrong with this service box, what needs to be fixed, and also its dangers if any... Can a wire cross over a bus bar?

Well, the red conductor on the left of picture #1 and picture #2 show pits, burn marks and split insulation.

I don't see the wire size on the red wires, so no, I cannot guestimate the max amperage load based on conductor.

It looks like you have a fuse panel instead of a breaker panel. If so and the red conductors are the ones from the meter to the panelboard, then if they are labeled with their amperage you will have your service delivery amperage. You just need to know one fuse size. They are not added together.

No, conductors should not cross over bus bars. But that speaks more to poor workmanship.

We could do a little better if we had some full shots of the panelboard. Personally. Since it is a fuse panelboard then just because of age I would want it replaced with a Main Service Breaker panelboard sized for your residence.

The current minimum amperage for a stand alone residence is 100 amps