How financial system works in UK? Must England, Scotland, Wales and North Ireland, fill the common budget or every country is completely independent, "keep" his money/profit for itself? Does the taxes fill the same UK budget or every country has own?
The Westminster Parliament creates a budget for its responsibilities that covers the whole UK. This budget will include taxes, money from other sources (such as bond sales) and allocations of money.
The government will allocate some money to the Scottish Parliament and Welsh Assembly. It will also allocate some money to county councils in England, and some to Schools etc.
Most of the money that the Scottish government spends comes from the block grant from central taxation. Scotland, for example, is a net beneficiary. In 2020-21, Scotland raised £62.8 billion in tax compared to £99.2 billion of public spending for Scotland (this was higher the previous years due to pandemic spending). But generally the flow of money is from the richer parts of the UK towards the poorer, and many of the richer parts are in England.
The local councils will then be able to raise more money from the "community charge" (a property tax). The Scottish Parliament is also able to raise some money by setting a different income tax to that in England.
The devolved Parliaments and the local authorities will then set their own budget on how they will spend the money on their areas of responsibility. However local authorities are subject to audit by the central government. Other public services will get their own allotment and will set a budget on how it is spent. Each school, hospital trust and police force will have its own budget (but they don't have tax-raising powers)
So the system is mixed. Most levels of government have some ability to raise money by taxes, but much of the money is collected centrally and allotted to local councils by the central government.