After my collection of 'Yggrasil Treeship' information from the novels that it came from, I've looked into inspiration pictures for it.
Here is a inspiration map to highlight some aspects.
And these are some key aspects.
The Norse 'Yggdrasil' is a towering monolith of a tree so I feel that the scale is very important. It needs to dwarf the mechanical components yet still feel apart of it.
The habitats must be futuristic and as of that I see them as the domed type hubs. These seem to be the most 'realistic' Interpritation due to NASAs research into the field.
The Hawking Drive seems to be that it doesn't equate to the engine itself. It's an extenstion of the engine.
The containers of the alien propellent system, the Erg, are imagined as just that... Containers. All though hinted at in the novels, that the inhabitants of the tree are communicate with them on some level, it's not confirmed. Due to that, I imagine that the creatures are almost forced into the situation.