A quick question.
Why is the gauge of most of Hong Kong's MTR Rapid Transit lines 3mm narrower (1432mm) than the lines of the former KCRC railway lines and the mainland Chinese railway lines (1435mm)?
Probably to ensure that there was a paperwork barrier keeping MTR as a self-contained metro system free of being tangled up with through running to/from conventional railways.
A non-standard gauge was chosen for BART (1676mm, i.e. Indian Gauge) for similar reasons, to prevent it getting tangled up with conventional railways while still being aligned with a large enough base of other railways (Indian Gauge is the #3 gauge in the world ranked by track kilometres) to allow economy of scale in production of components.
Also can a wheel be designed that allows running on both gauges?
For sure, in fact I would bet that every MTR train uses exactly the same wheelset profile regardless of which lines they run on.
Remember that the coned profile of wheels and lateral movement is how trains negotiate curves on a railway, so movement within the gauge is entirely normal.
In Eastern Europe, the slightly different 1524mm (Estonia and Finland) and 1520mm (most other Russian-influenced countries) gauges are treated as being compatible.