Items that you don't have room to receive from a trade like this are placed into your overflow inventory until you do have room and change worlds. This is expected behavior.
I cannot tell what the method of reproducing this issue is supposed to be. If you can update this with more specific steps and the context in which this issue is occurring, I'll take another look.
There's not enough information here to tell what you're seeing, "glitchy" isn't very descriptive and I'm not seeing any issues when I look at this mount's VFX.
Unless there is somehow a case that this is actively harmful to the player experience, I don't think we'll be fixing this. The edge case where it can become invisible requires a good bit of setup to accomplish and doesn't seem to break anything else.
After following the repro steps as written, when I right click as directed I perform my M2 ability as expected, rather than remove my hotbar item. I checked this against a few different types of items and several classes. Are there any mods you're using that might be affecting this?
I can't reproduce this issue based on the information you've provided. In your screenshot it looks like you've been repeatedly pressing the key that would activate your fishing rod, and you're getting the message that your inventory is full. You're not standing near the shadow vault, nor do you have a key on your hotbar. More details as to what happened here would help clarify what you were doing and what you expected to happen.
I cannot reproduce this issue with the provided information. Make sure that any mods you're using are up to date, and if this continues to occur, please update this issue with more specific information about when and where this happens.
There isn't enough specific information to reproduce this issue. It is known that there are some weird behaviors with coin challenges and we're looking into them when we have time. If you can provide a consistent repro for this I'm happy to take a look again.