It's a great question. This subject is covered here
In sum, you have a choice (explained in the link above). My guidance would be:
serving as a Sovereign ?
the extent the Sovereign can exercise power ?
[no need for a capital letter in this case. I do not judge this to be a proper noun]
Head of Executive, Head of Judiciary ?
[I would leave these as they are. They are job titles; therefore, proper nouns.]
part of the Legislature
[I would lose the capital letter in this case. I judge this to be a common noun.]
calling and dissolving Parliament and emergencies passed to the Parliament
[Now, this is a hard one. You should be consistent, but I fancy a capital for the first one, but not for the second. Use capitals - my advice.]
The question you need to ask is:
Is it the name of something (proper noun) - if yes, use a capital.
Is it the name for something (common noun) - if yes, use a capital.
There is the etiquette to consider too. It's a difficult subject. My overarching advice is go with what you judge to be correct and be consistent.