The 'Missing parts,' that Tyr told the captain about when 'the incident' occured were maybe the Neurals Tyr had installed into whatever he created to 'control and/or contain' the Mæron when it's in use. Those missing Neurals were somehow combined with the Mæron itself, maybe some of the crew that were in its vicinity, and possibly the mind and body of a being from another universe/time/galaxy/reality. Which created the being that calls itself Tucker. That's why he can understand them, that's why he's having these random visions, crazy dreams, memory issues, hallucinations, etc. That's why the cleaning robot and now the 'mascot' are coming after him. He has their 'minds' and they're trapped inside some machinery and in Tuckers mind. Now we have some sort of Tuvix situation with Tucker, the Mæron and whatever else combined to create him.
I always get excited when I see a comment of yours. I've said it before, but it's worth repeating: I love the way you think, it is familiar, like seeing someone saying the things I don't have the words for.
When Tucker had his first hallucination I thought "he fused with the people who created the Mæron or the dead minds of the people who worked on it got absorbed by it and then installed on Tucker's mind when he got abducted"