The Panic Necklace is especially useful at the beginning of the game if Hermes Boots (or their upgrades) have not been obtained, as damage taken from enemies will provide a great speed boost. If paired with a Sandstorm in a Bottle, the double jump from it will go much farther than usual for the duration of the Panic!

The Panic Necklace is an accessory that gives the Panic! buff after taking damage from any source, raising the player’s speed. It is dropped by Pulsating Hearts in The Crimson.

The Cross Necklace is useful in Hardmode boss fights and any other scenario where the player is likely to be hit rapidly, such as Destroyer or Skeletron Prime.

The Band of Starpower can also be obtained by fishing for Corrupt or Defiled Crates. Nintendo Switch version, the Band of Starpower can be crafted in the Graveyard, from a Panic Necklace and a Mana Crystal. tModLoader version, an artificial Corruption can be created to fish for the Corrupt/Defiled Crates.

In simple words, cross is a Christian religious symbol and is said to signify faith, good luck, and fortune. The cross pendant is believed to protect its wearer from harm, bring calm and peace, and ward off evil spirits.

But to answer your question, yes, it will drop pre-hardmode.

The Jellyfish Statue is a functional statue found underground. When wired to a trigger and activated, the statue will spawn Blue Jellyfish. Three jellyfish can be spawned before there is a short cooldown. Afterwards, three more jellyfish can be spawned.