A fresh new captain.

I want to start a new game. But I do not know If I will keep the special items like the dream in red or the codex. Anyone knows it?

You only keep your Legacy items if your captain dies or retires, and you create a new one that way! If you start a brand new game from the main menu, you won’t inherit any Legacies.

Can I retire without an Ironclad will and retain them?

I believe so, as the Ironclad will only relates to your lodgings and any heirlooms in them; retiring without it will reduce you to lowest housing if you decide to retire/draw with your current captain.

Sort of in order of what you can keep for New Captains

A brand new captain - no items except the things that you can get from linking to Fallen London - Whisper Locked Chest; Soothe and Copper Long Box; M Demeaux’s Advice and a Parabolan Kitten (or Panther if you were a backer at that level).

If you die or retire

Half of a stat and either a weapon (Iron); half your money (Mirrors or Veils); an Officer (Hearts) or your chart (Pages)

Any Legacy items you have found with previous captains

When you have a Townhouse you can write an Iron Clad Will that lets you keep your house, or Mansion when you get one, and any Heirlooms you have created.

Also when you get a House you can raise a Scion and that will let you choose two stats options.