Some help for a noob

[Skandranon]

Do I just go in there from Westfall's entrance (to which I escorted the Traitor), or do I talk to the innkeeper in Stormridge, or what else do I have to do?

Going into the area to which you escorted the Traitor will get you into a fairly extensive "pre-instance" area: a world location (i.e., not instanced) full of elite mobs. Inside this pre-instance area is the portal to the actual instance: it appears as a glowing, swirling white bounded space. The Deadmines pre-instance area is fairly tangly and relatively long, but if you keep going down, you'll find the portal.

Usually the pre-instance area is kept relatively clear by the groups that keep sweeping through it on the way to the instance, but if it's not, you'll find it's a bit slow going, especially soloing at 24.

If I die, do I have to run to the body as usual, or does the instance end, or....?

If you die, you need only return to the instance portal. You will be resurrected the moment you step inside.

If I res at the cemetary, and deside to forget about it, do I have to reaquire the quest again? Can I even do it?

Quests cannot be permanently failed in WoW, and that's for failable quests. If you don't get the quest done the first time you go into the Deadmines, just go again, and again, and again. Instancing is only meant to keep other people out: you are not limited to one instance per lifetime of character.

What is the difference between a Dungeon and an Instance, as illustrated by the monster info shown here:
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There is no difference. The page you linked expresses monster locations two different ways through a quirk in the software.