1. Are there any secret stations ...ie that were not supposed to know about
There are some who believe there is a secret Underground station at Buckingham Palace, but there is no actual evidence of this.
On the Piccadilly, it was Down Street that was used as a bunker during WW2 but was subsequently returned to LU. This isn't the case at Brompton Road, where the surface building remains property of the MOD, with access only at track level for LU staff.
2. Are there any disused stations that are visible on a normal journey (not temp closures)
Yes. On the tube lines, it's possible to see some closed stations. If you look closely out the windows you can see the tunnels widen out, where the old platforms have been removed, e.g. British Museum or South Kentish Town. At some places, such as Down Street where the station was converted for other uses the platforms have been walled off, or turned into sidings (or both). In most places, some original tiling also remains on the tunnel wall, but is obscured by dirt - sometimes you can spot it if the train is going slow enough.