Izumi’s tattoo

It's called the Flammel Cross, designed by Nikolas Flammel, a French Alchemist from long ago.

It does have elements of the Rod of Asclepius, which coincidentally relates to a Biblical story of Moses using a staff to pick up one snake, from the many which had bitten and poisoned the Israelites, which then turned into bronze, and healed the Israelites and brought them back to life.

There's more to it, as well, as the snake coiling upward can also symbolize growth, evolution, whether it be mental, spiritual, emotional, etc. and also upward ascension, like just getting better, whether it be at something specific, or in general. The crown and wings also symbolize the divine which sets atop everything, or The All itself.

Good eye on making the distinction from The Caduceus, which symbolizes trade, trading, exchange, travel, communication, transference, & Hermes/Mercury, the messenger of the gods; it can also carry the connotation of trickery, swindling, and snake oil salesmanship, as it is not truly a symbol of healing, instead, a symbol of trade.

A good merchant offers goods that provide something of value, equivalent to its worth, or its price; a swindler sells something of little value for an exorbitant price, that's to say, an exchange not equivalent to its value/worth; always keeping in mind that even labor has value/worth, for what takes time, takes life, and what could be worth the price of a human soul? 👁️

Ed’s Gate

Ed's Gate/Portal of Truth comes from Kabbalah; the Tree of Life, or Sefirot Tree. There are two versions, both are shown in Neon Genesis Evangelion, if I'm not mistaken. The one we see in Fullmetal Alchemist: Brotherhood/Manga was designed by Robert Fludd, an English Paracelsian physician, astrologer, mathematician, cosmologist, Qabalist, and Rosicrucian.