The Transport Department of Hong Kong now maintains a Special Traffic News page that contains up to date information on surface and public transport, including on the MTR.
As of the time this answer is written, the page contains the following entries:
Airport Express is running normally between Hong Kong, Kowloon, Tsing Yi, Airport and AsiaWorld-Expo stations.
Starting from 11pm, Airport Express will be running between Airport and Hong Kong stations only. Trains will not stop at Kowloon, Tsing Yi and AsiaWorld-Expo stations.
Please allow more time for travel.
In-town Check-in service will be suspended at Kowloon Station starting from 10pm. In-town Check-in service at Hong Kong Station will remain normal and please allow 90 minutes ahead of the scheduled flight time for the check-in service.
Train service on all MTR Lines (except Airport Express), Light Rail and MTR Bus will end at 11pm today.
For barrier free access, please contact the station to check the status before travel, as barrier free facilities may not be available.
Please plan your journey accordingly.
The OP also asked:
[I]f I'm riding the MTR while reaching the closing time, what happens?
Approaching the early closing time, trains may stop short of the end of the line (say in a station immediately preceding the depot/sidings), staff may shoo you off the station, and you should then consider other transport options (e.g. Night buses, taxis).