A constitutional monarchy does all those things.

And they are not republics, but can be democracies.

True, I stand corrected :) .

What I wanted to say is that the OP was describing a divison of powers as commonly seen in a Republic, it was not something inherent in a democracy.

All republics that actually are republics are democracies; true republican government is a form of democracy.

All republics might be democracies, but not all democracies are republics, which was my point:

http://en.wikipedia.org/wiki/Direct_democracy

http://lexrex.com/enlightened/AmericanIdeal/aspects/demrep.h...

Right. Democracy is subclassed into Republic and DirectDemocracy; Republic is further subclassed, one such subclass among many being CrownedRepublic, such as the UK.