Regarding the lift mechanism, I suggest you look at the semiconductor wafer-handling robots. You can see the insides of one version here: https://www.ifixit.com/Teardown/Hine+Design+Inc.+Automated+Wafer+Handling+Unit+Teardown/1651
In that robot they used a lead screw vertical drive mechanism along with (it looks like) two cylindrical shafts for stability and linearity. When I've built systems using parallel rails or shafts, it is very difficult to keep them collinear, so we would usually fix both ends of one rail, and only one end of the second rail. The other end could float over a small range. That way we would prevent binding due to misalignment issues.
That industry has made vertical lift mechanisms for robots out of everything from pneumatics, to linear motors, to ball screws, and more. All of their designs require compactness and cleanliness, so some of the designs are very clever. You can search for patents by companies such as Genmark, PRI Automation, Brooks Automation, Applied Materials, KLA Tencor, Hine Design, and Adept to find good examples.