Metro

Yes, they are open normally.

Why Google map said the metro stations are permanently closed?

I guess they have made some mistakes. You can also try Bing Map.

What should I do, I have layovers between 5pm and 8am and again between 10pm and 12 noon?
Metro are closed between midnight and 6am

Is it safe to walk between midnight and 6am around canton tower area?
Are there roast goose and Tim sum around this area?

Do express buses run from canton tower back to the airport between midnight to 6am when the metro are closed ?

Yes, it is very safe. At about 6:00, some restaurants are open to offer Tim Sum but I'm not sure about Roast Goose.

The first train of Metro Line 3 departs at 6:12 am. You can take Metro Line 3 from Canton Tower to Tiyu Xilu Station and then transfer to Metro Line 3 (North Extension) to the airport. There is no other direct bus to the airport at that time.