The PM is the head of government and is ultimately responsible and accountable for its actions and policies. They are also the head of their political party and thus will have a say on what policies are brought to the table (although they do still need to be voted on in the houses).

Our PM is not technically the head of state (that’s the King, from whose power the government derives its authority), however for all intents and purposes they may as well be.

So yes, his resignation will have an impact.

You really gonna do the Blades dirty like that?!

I think you may have Europe confused with Japan.