Can you only make specific classes in specific campaigns?

So the image I have this far is that you can start from any Campaign but you can still do all the quests in the game. Also campaigns add classes

So I would like to know if I could make an Assassin in Prophecies etc.
Thank you.

You cannot make an Assassin in Prophecies.

The six core classes (Monk, Mesmer, Elementalist, Warior, Ranger, Necromancer) can be made in any campaign.

Assassin and Rituatlist can only be made in Factions.

Dervish and Paragon can only be made in Nightfall.

You cannot start a character in Eye of the North.

You can go everywhere and do everything with any character from any campaign, excluding some of the very early starting areas in Fact. & NF and of course Pre-Searing in Proph.

You can do most of the quests in all the campaigns, however, the beginner ones usually are available only to those characters who started in that chapter --at the point where you can join the other chapters (lion's arch and kaineng center) there will be quests that all characters can do (kamadan is different --there is a nightfall character quest line and a non-nightfall character quest line).
If you check out the wiki it will usually tell you if the quest can be done by any character, profession specific or chapter specific (nightfall only, factions only, prophecies only).
All missions can be done by all characters, however, low level ones non-chapter characters will get no xp for mission completion.
And eye of the north is an expansion, so all characters can do all the quest/missions when you are able to access it (level 10 requirement).

As far as mission towns go, you can travel to the starter island in Factions to complete the two missions there (exit Kaineng north west entrance Bejunkan Pier, up and down the stairs and talk to the npc down there, I forgot who it was though) and in Nightfall you can do the same.

Thank you for the helpful answers.