That is the case if the Guard is working from a local door panel, but if they are working from the Cab of a 377/6 or 377/7 and I believe also the older 377's, then they cannot close the doors from there themselves and have go give the 1-2 bell code to the driver. Happens quite often on peak services where it is too crowded for the Guard to work safely from the passenger saloons!
Yes, that is the case on all 377s. The signal bell is the only button which works on the door controls in any cab other than the driver's. There is, however, a way of telling that the doors are released or closed (but nothing which you would formally describe as an interlock indication either - BIL lights are used as indicators by the guard, then the driver checks their interlock light).
On 171s operated by Southern the guard releases and closes the doors, except if the driver would like to open or close the doors on empty stock where all coaches are in the platform, in which case a clear understanding must be reached with the guard. However, the guard does not get an interlock light of any sort on these either, but instead the buzzer will not sound unless interlock is achieved (in other words, you cannot give "2" unless there is interlock).