What would be the average distance between each 1-degree latitude on Jupiter? Do planets like Jupiter have a system of latitudes and longitudes (I believe yes)? So if yes, what purpose do they serve? Is there anything different in their purpose from Earth lat-longs? and What would be the average distance between each 1-degree latitude on Jupiter?
Yes, they have coordinate systems as well. For example, the Wikipedia page on the Great Red Spot mentions it lies 22 degrees south of the planet's equator. Jupiter has a polar radius of 66,854 km; a latitude degree is $2 \pi / 360$ times that, so almost 1,167 km.

Note that because Jupiter lacks a solid surface, longitudes are less well-defined. In fact, there are three different systems for this:


  Because Jupiter's visible features do not rotate uniformly at all latitudes, astronomers have defined three different systems for defining the longitude.


Rocky planets like Mars do have a well-defined coordinate system, as shown in this map and on this page.

These coordinates are used to mark and find interesting places on either the surface (like on Earth) or in the atmosphere of a planet. There are also tables available showing which latitude/longitude is directed towards us at a certain moment, so that you can compute whether a particular region of the planet is visible from Earth or not.