Let say I have a Mizzium Transreliquat using it's second ability to copy a Bonesplitter and I have it attached to a creature. If I use it's second ability later on, like before damage in combat, could I turn it into a another equipment, like Sword of Fire and Ice, and have it still attached to the creature?
All you described is legal. It would be unattached if Mizzium Transreliquat turns into creature or changes into something what is neither aura, nor equipment that can legally be attached to what it is currently attached to
Quote from 704.5q »
If a creature is attached to an object or player, it becomes unattached and remains on the battlefield. Similarly, if a permanent that’s neither an Aura, an Equipment, nor a Fortification is attached to an object or player, it becomes unattached and remains on the battlefield.
Standard Curses
Satsuki-Extraction-Puppeteer-Cruelty
Explorer Stun Counters Proliferate
Azor-Feather Blink Control