I'm confused about the use of the Dueling Sword. I have an Elven Rogue with Weapon Finesse, but without the exotic weapon feat nor heirloom trait, etc.
Since the rogue can use the weapon as Longsword, can the Weapon Finesse feat still be applied or is the Dueling Sword a plain Longsword?
No, since the description you provided says that: "If you aren’t proficient with the Aldori dueling sword, you may treat it as a longsword."
I read that as saying with proficiency you cab can use WF and without it, No