This question is a few years old now but I felt the other answers weren't quite hitting the mark so I thought I'd add some fundamentals. It's necessary to understand "where the money goes ultimately".
Note that the below is from a heterodox economics perspective incorporating aspects of modern monetary theory backed up by empirical research and understanding of banking operations
When the US government decides on its policy objectives, it establishes an annual budget via Congress. This budget represents the amount of money required to achieve its objectives over the following year. A large amount of this will be for non-discretionary payments (eg. social security, welfare, medicare, etc), another big chunk will be to hire the labour of people to carry out the gov's priorities, and some more will be to buy raw materials, products, or services from people or organisations that the government will need.
The next step is that the US Treasury will instruct the Federal Reserve to make payments. This involves the fed increasing the value of USD reserves held in the fed account of the bank of the individual or organisation selling the labour, good or service. The Treasury's account at the fed is debited the same amount. That commercial bank will then make a corresponding increase in the deposits held by the individual or organisation at that commercial bank. See Fiscal Data from the US Treasury for an overview of this spending process and the breakdown. The key is The President and Congress pass laws which mandate spending to occur. Also, see Tymoigne 2023; pg 17:
central bank routinely helps finance the Treasury... it just ensures that the Treasury has enough funds to implement the budget passed
The end result of this transaction is that the seller's net financial assets have increased (more money in their bank account with no increase in liabilities), the commercial bank's liabilities have increased (i.e. they now owe the seller more money should they wish to make a withdrawal), and their financial assets have also increased, with a higher amount of USD reserves held in their Federal Reserve account. So the bank's net position has remained unchanged.
The above is how all government expenditure occurs on a mechanical level.
However, if nothing else changes, this expenditure can eventually result in too much demand for the supplied goods and services in the economy and the price level will increase to compensate. Inflation occurs.
To address this, the US Government proceeds to use its legal authority to apply tax liabilities on people and organisations. By reducing the amount of USD available, the Government is decreasing the financial ability of actors in the economy to spend, thereby reducing the demand for goods and services in aggregate. This acts to counter the increased demand pressure caused by the preceding Government expenditure. The aim is price stability, or more accurately, a low and stable, but positive, non-zero inflation rate. See Baker et al. 2020 and Tymoigne et al. 2013 for more on the role of tax. Also see Tymoigne 2023; pg 17
...national government that issues the domestic currency, and taxes and
issues securities to destroy the currency
However, historically each year (apart from a few exceptions), the government fiscal balance has been in deficit. This is a non-government surplus. The surplus refers to the fact that the money supply available to the non-government sector has net increased as a result of spending more than is taxed away.
This is often a good thing because, as economies grow, they need more money to facilitate the increased number of transactions and stocks and flows of goods and services. This is evidenced by the fact that the US non-government sector has experienced a surplus almost every year of its existence (see FRED US government deficit data) and yet standards of living and the productive capacity and capability of the US economy and society is far higher than it was in the past.
Now, so far, I've mentioned nothing about bonds. This was on purpose as ultimately, Government bonds are a less vital part of the monetary story.
By historical convention (and two further primary reasons given below), the US government decides to sell US Treasury bonds to cover any deficits it runs. The Treasury creates the bonds and issues them via auction to commercial banks with reserve accounts at the Fed (see How Auctions Work for an explainer). The purpose of issuing these bonds is to provide a risk-free saving vehicle and to help the central bank achieve its interest rate target. Remember, the reserves (commercial bank assets / central bank liabilities) used by the commercial banks to purchase these Treasury bonds were placed there when the Government spent on its priorities and instructed the central bank (monoply issuer of USD reserves) to create them. See The Fed Explained, specifically page 86:
The Reserve Banks also act as fiscal agents of the U.S. government and certain other entities. In
other words, they act as the “government’s bank” and maintain the operating cash account of the
U.S. Department of the Treasury; process payments to and from the Treasury’s Federal Reserve
account; and issue, transfer, and redeem U.S. government securities.
See also Tymoigne 2014; pg 9 following a detailed analysis of federal reserve and US Treasury operations:
issued securities for other purposes than funding itself. One reason is to provide a means of
payment for the country; another is to help the Federal Reserve in its interest-rate stabilization
operations; a third one is to help financial institutions meet their capital requirements and to
provide a foundation upon which all other securities are valued by providing a proxy for the
So quite literally, bond issuance is a process of 'mopping' up excess reserves in the system that the government put there.
So, in a directly analogous way to how tax revenues are destroyed/deleted, the reserve dollars used to buy government bonds are simply destroyed. The money doesn't go anywhere.
Current budgetary procedures do require, by regulatory convention, the Treasury to issue Treasury bonds to cover any deficits, but this is an artificial and political requirement, not a fundamental economic requirement.
How separate is the Central Bank budget from the government's budget?
As a shorter exposition on your second question, it is important to recognise that, while the US Treasury and Federal Reserve are operationally independent, they liaise closely with one another daily to coordinate fiscal and monetary operations (since the federal reserve is factually the government's bank and fiscal agent).
It is misleading to say the federal reserve has "a budget". It holds assets (eg. Treasuries it bought with newly created reserves via Open Market Operations (OMO) see The Fed Explained again) and liabilities (primarily electronic reserves held by commercial banks).