elec strike and This kind of Lock

As far as I know, all electric strikes meet your critera. The e-strike is mounted in the frame, not the door. Wood frame applications are the most difficult. The model strike will be determined by the kind of hardware on the door. E-strike and door lock are 2 different things. We need more information.

Bob

Surely an 'electric strike' meets all these criteria since it is mounted on the doorpost and allows the usual doorlock to operate unimpeded.

Lockwood (Australia) makes a mechanical with electric release door lock which has the above features. See:

If you're talking about an electrified strike, it by definition meets all those requirements since it modifies the door frame rather than the lockset, and the lockset continues to support all its normal functions.

If you prefer an electrified lock, it's possible to get these behaviors that way too; it's just a matter of ordering one with the right locking functions, much as you have to specify the function when ordering a non-electrified lock.

If you prefer a magnetic lock, that gets more complicated; you need a sensor on the inside to release the magnet for exit and a keyswitch or other mechanism to request entry from outside.