Possibly. An injunction is a court remedy, not something a Party Wall Surveyor grants. It may be sought where notifiable work is threatened or underway without the required statutory process or where other property rights are at risk, but the court applies equitable principles and the facts matter.
No. The Party Wall Act procedure cannot be used to determine where the legal boundary lies. Surveyors may need to understand the assumed boundary to deal with statutory work, but a genuine boundary-title dispute requires agreement or determination outside the Act.
The death changes the ownership and authority landscape; it does not create a simple statutory shortcut. Identify who now represents or owns the building owner's interest, whether the proposed works are continuing, and whether existing notices, appointments and awards can still be relied on before further statutory steps are taken.