Is there any point in raising your guns or melee skill because I have not noticed any damage increases even when I leveled the skills up. Does it give you increased range and accuracy, that kind of stuff?

Well there is the small incidental factlet that some weapons require a higher skill rating so they can be used effectively.

You oughta try levelling them up and see what happens... That being said, my fave character so far is a pure scientist... No skillups on any combat skills, just science, repair, lockpick, etc... I travel with Raul and EDE and they take down nearly everything for me.