Can I use an old humidor today?

You can certainly use one for daily cigar storage. The core mechanics of a sealed wooden box remain the same today as they were a century ago. Most older boxes just need a period of re-seasoning to function well again. The dry wood needs to absorb moisture before it can maintain a stable environment. Wipe the interior gently with distilled water and leave a damp sponge inside for a few days. Once the cedar reaches the right humidity level, it will keep cigars fresh.

I got this big wooden box from my grandad that has glass jars inside and a sort of metal rack thing, is that still a humidor or something else for tobacco?

That sounds like a smoking cabinet rather than a standard humidor. Late nineteenth-century makers often built larger pieces to hold pipes, loose pipe tobacco and cigars together. The glass jars usually held the loose tobacco. The metal rack was likely a pipe rack. While these cabinets kept all the smoking gear in one place, they rarely offer the tight air seal needed to regulate humidity for cigars over long periods.

Why is my humidor lid sticking?

A sticking lid usually means the internal wood has swollen. The inner cedar lip expands when the humidity inside the box gets too high. Leave the lid open for a few hours in a dry room. The wood will shrink back as it loses moisture.

My uncle left me this heavy wooden cigar box but the little dial on the inside of the lid seems stuck on one number no matter what I do with wet sponges, can it be fixed?

The dial is a hygrometer, and older ones rely on a coiled metal spring. Over time, constant dampness can cause the internal mechanisms to rust or seize up. You can sometimes revive them by wrapping the dial in a damp cloth for a few hours to loosen the spring. If that fails, it is often best to leave the original dial in place for appearance. Many people just hide a small modern digital sensor inside the box to track the moisture instead.