If the exterior walls (red) are expanded and the interior walls (blue) are stroked paths you will not be able to get the kind of snapping you are wanting.
If both exterior and interior wall paths are expanded you can go to View> Snap to Point and then grab the path you want to move by the corner you want to join and it will snap to the other path corner ...
A brute force solution.
Have a corner adapter with new anchor points inserted to the right places:
In this case the stroke widths are 2,5 mm and 5 mm. The green adapter is a 5 x 5 mm strokeless square which has got two times Object > Path > Add anchor points.
The exact placement on an unexpanded stroke is based on the centerpoint of the adapter, so ...
Yes, it is. Select all single paths and then combine them into a compound path by pressing
Ctrl+K or from the menu using Path → Combine.
(Later you may break them apart into separate paths by clicking Shift+Ctrl+K or from the menu using Path → Break Apart.)