Has monarch extraordinary economic prerogative? do gov. consider a (very small) part of budget for queen and royal family?(besides what is for all people)
Has monarch extraordinary economic prerogative?
The exact power of the Queen is somewhat unclear there is a number of posts on this site suggesting the Queen has all the power. However, in practice the queen tends to enact the legislation the government puts forward and hence in effect would seem to have limited power or at least she don't appear to use it.
The Crown is exempt from tax as are the duchies of Cornwall and Lancaster. However other members of the family pay tax in the normal way including the prince of wales (except in respect to the Duchy of Cornwall). It's worth noting that the Crown does pay tax on a voluntary bases based on a memorandum of understanding the exact details of which are unclear but are supposedly equivalent to what other people pay after the crowns official expenses on taxes including income tax and in some limited cases inheritance tax and capital gains tax more details here.
do gov. consider a (very small) part of budget for queen and royal family?
The queen receives the Sovereign Grant front the treasury. This is a percentage of the income from the crown estates (The crown estates are the estates that belong to the crown but not the Queen or members of the royal family personally). This has temporarily increased in recent years to cover renovation costs including that of Buckingham palace. Details of the royal families finances and how the crown has been funded previously can be found here.
It's also worth noting
The Sovereign Grant does not cover the costs of Police and Army security and of Armed Services ceremonial security. Nor does it cover the costs of royal ceremonies or local government costs for royal visits.
These costs are presumably covered by either local government or the relevant government department.
Edit - the crown estates
The crown is a corporation sole this allows that the possessions of the crown and it's respective powers to be passed between physical persons (legally speaking a corporation can also be called a ('legal') person). This means that the crown continues as an entity even when an individual holder of the office passes on, hence, the authority of the crown continues uninterrupted. However much like anyone else who owns a corporation (or holds an office) the holder of the crown is also entitled to personal holdings.
The crown estates belong to the corporation sole that is the crown, this is a legal entity in and of it's self. The queen or other members of the royal family may also have estates outside of the 'crown corporation sole', incidentally these may also be wrapped in a corporation of some kind.