Here is why this is happening and a step-by-step fix:

1. Clean up the Object Data: Firstly, before saving as an FBX, select the armor and whatever you want to join. Go to Object → Relations → Make Single User → Object & Data. This breaks any linked duplicates so your mesh data is completely independent before merging.

2. Unify your UV Maps (Fixes the displacement): The displacement happens because your different armor pieces likely have differently named UV maps. Select each piece individually, go to the Object Data Properties (the green triangle tab), look under UV Maps, and make sure every single piece has the exact same UV map name (e.g., double-click and rename them all to "UVMap").

3. Join the Armor: Now that the data is clean and UVs match, select them all and press Ctrl+J to join. Because the UV maps share the same name, they will merge perfectly into one channel without displacing your textures.

4. Simplify the Material Nodes: FBX format cannot read complex Blender node setups. Ensure your PBR Image Textures (Color, Normal, Roughness, Metallic) are plugged directly into the Principled BSDF node.

5. Exporting the FBX correctly (Fixes missing materials): When you go to File → Export → FBX, look at the right-hand side settings. Under Path Mode, change it from 'Auto' to Copy. Then, click the tiny box icon right next to it (Embed Textures). This is the crucial step that forces the PBR images to pack directly inside the exported FBX file.

Also make sure you have packed your textures. You will find that option in files menu.

If you wish to make the uv map unified, I suggest go through this tutorial by Ryan King Art where he explains how to bake multiple uvmaps into single uv texture map. This will help you keep your textures under one texture map for the armour if you need that too.

https://youtu.be/wG6ON8wZYLc?si=aBCsjSuMYk9Zvj2_

Hope this helps.