can a caretaker PM wage war?.......................
Legally speaking, he can even unload India's entire nuclear arsenal on Pakistan.
One does not become a caretaker PM when model code of conduct is in effect. PM remains a full-fledged PM till current Lok Sabha superannuates (on 25th May). There are only restrictions on certain policy-making, but national security is out of its scope.
However, let's say we're at war, and Election Commission tells the President that General Elections cannot be executed. In that case, President declares a state of Emergency, and appoints a caretaker PM to govern seamlessly after Lok Sabha superannuates, for the specific task of tiding over the emergency; whilst the country's day-to-day governance is in the hands of the Executive/bureaucracy (i.e. President's rule).
President has other fascinating powers such as appointing a Field Marshal.