Syringe, yes. I got it. It is a main hand weapon. It may not be very visible depending on your graphics setting though because with the Plague Doctor Outfit, your character puts his main hand behind his back, so the Syringe may look like a green dagger or small sword to you.
The 3 outfit variants can be found in the Customizations - Wardrobe window. By clicking the "Full Outfits" button, you can select to wear one of the full sets. The appearance will show, regardless of what you are wearing.
The cane and syringe main-hand can be found by selecting the main-hand customization. You will need to be wielding an appropriate item for the override to show. Wielding nothing will show you empty-handed.
The off-hand syringe is in the off-hand customization. Likewise, you my be wielding...
As for bug reporting, click the gold flag with the X on it. It's in the top right area of the chat window, in my case. You select to report a bug, not report a player. You'll get to a place where you can type about the bug and its recreation steps, if applicable.