what can you do to party wall without party wall act

[annoyednow]

Just wondering as in this long saga, attached neighbours have been hammering on party wall and have removed plaster and the wood strips in their side of party wall. This is allowed isn't it? If they cut into brick for supporting beam this is not allowed though, right?

Also just wondering about something. There is a chimney stack on the party wall which serves the flues on our side of attached property exclusively. Is there meant to be a protrusion on their side of party wall down to ground to support this stack?