Do new playthroughs require new characters?

I've never played Diablo 2 before. If I beat the game and then restart on a harder difficulty, will I be reusing the character from my first round through the game or making a new one?

Every character has to go through the game modes on its own. Every character starts in normal, once that is beaten can then enter nightmare with all his gear and levels intact. After beating nightmare you can enter hell.

All the difficulties contain the same monsters/areas/quests. The map will have a different layout, but blood raven will always be there. Just as the countess. And all the other bosses. Monsters do NOT scale to your level at all. They get extra immunities/resistances in higher difficulties. (for example fallen are immune to fire damage in hell)

If you somehow get a level 1 character into nightmare or hell he will be one hit killed by everything.

yes, you will.

But don't forget that there are some "penalties" in higher difficulties. In Nightmare you will get -40% to all resistances and in Hell it will be -100%.

Also don't forget that the levels of the monsters are higher in higher difficulties. For example, a Pit Lord will have level 27 in Normal difficulty and level 83 in Hell. Also it's hit points will grow from 200-ish to 9-14k-ish.

And if you hack you character or if you play online, you can even get a level 1 character in Hell. In this case I'd recommend you joining public Chaos Sanctuary runs till level 20, then public Cow Level runs till 25, then again Chaos Sanctuary runs till 60, then do Ancients quest in Hell and level up in public Baal runs.

Source: level 99 Battle.Net paladin