S1:
The collapsed house will be rebuilt in two years.
(I think S3 is grammatical as well but sounds less natural.)
T3 means the same as T1.
T2
The picture, having been torn into pieces, can no longer be sold. = Since the picture has been torn into pieces, it can no longer be sold. = The picture can no longer be sold because it has been torn into pieces.
T4
The picture being torn into pieces by those scoundrels is very valuable. = The picture that is being torn into pieces by those scoundrels is very valuable. = The picture that those scoundrels are tearing into pieces is very valuable.