That has absolutely nothing to do with whether it is a democracy or not. A republic is a country that is that is not governed by a king/queen. If a country is not a monarchy, then it is a republic.

If people vote for leaders to make decisions on their behalf, it is a democracy. If the people cannot vote, but are governed by some others, it is either a autocracy, pr a plutocracy, or an oligarchy.

You say that some laws cannot be changed, and that is what makes it a republic. I don't know where you get that idea, but that has nothing to do with whether a country is a democracy or not.

It is also erroneous - if you're referring to the constitution
There are conditions when something in the constitution can be changed.