Last time I got an update for neptune court was in March 2010 - abt them appointing a law firm to undertake the privatisation. It's a long process, still many negotiations and voting etc to go through. My guess is it'll still take some time before privatisation becomes reality.
Privatisation of Neptune Court & Lagoon view hav always received mixed feelings from their residents all these years.
Owners of neptune court (and all other HUDCs out there) will need to pay a lump sum not to SLA but to Ministry of Finance (which owns the land) should they be privatised (which is step 1 to a collective sale AKA enbloc).
[To put it simply, Neptune Court is a Housing and Urban Development Company (HUDC) housing which is under our government BUT falls FAR from the same category of HDB (different governing legislation etc).]
In regards to your last question, i might be wrong but all property ownership / title information are under SLA, which you can check at http://www.inlis.gov.sg.