Well, technically it would be a change in government, as the current one is Liz II ruling by the advice of her Prime Minister. Changing to a republic might be bloodless, but it would be a change of government even if that government remained a Westminster-type parliament with a differently-chosen ceremonial head of state.
Yes, you’re right. What I meant is that the prime minister and ministers would probably remain the same. There would be continuity even though the head of state would change.
The Petition of Right (1628) established that Parliament not the King could raise taxes. The same document also prevented arbitrary arrest, interference in property rights, billeting of troops in houses and imposition of martial law.