I will never understand how a president can have powers to change any government agency, any aspect of life, change international policy.

So, there are two types of "rules" in the US.

• The first is what in the US are called "laws" or "legislation". In the UK, this is called "primary legislation". This stuff is written by the legislature. The President can't change this stuff.

• The second is what in the US are called "regulations". In the US, this is called "secondary legislation". This stuff is written by the Executive Branch, which can change it. By convention, generally Presidents don't jump in and fiddle with it, but they can tell the Executive Branch to do whatever they want. Basically, Trump is ignoring a lot of convention surrounding what Presidents don't touch. You could argue that maybe we should change the system to permit for certain things -- like, I can maybe see an argument for the Federal Reserve to have some kind of aspect outside Presidential authority, because there are political incentives to fiddle with it the interest rate around elections -- but as things stand, that probably would require a constitutional amendment, which is pretty hard to get through in the US.

For international policy, that's pretty much the Executive. The Senate has to approve of treaties, but most of what we do internationally is the Executive Branch.

any aspect of life

I mean, they can't. There are a lot of restrictions on what a President can do.

1. Federalism. There are areas where the states have exclusive authority, and the federal government -- not just the President -- can't involve themselves in those. That's why Trump has tried to argue that he should be able to withhold federal funds contingent on states doing what he wants, because the states aren't doing so on their own. I'm skeptical that he's going to have a lot of luck with this in the courts. In the past, Congress -- which is on much firmer ground than the President when it comes to claiming ability to distribute funds -- has managed successfully to use the power of the purse sometimes (e.g. in getting state drinking ages up by withholding highway funds), but has also had its wings clipped, as with the health insurance mandate a while back.

   https://en.wikipedia.org/wiki/Power_of_the_purse

   The power of the purse has also been used to compel the U.S. states to pass laws, in cases where Congress does not have the desire or constitutional power to make it a federal matter. The most well-known example of this is regarding the drinking age, where Congress passed a law to withhold 10% of federal funds for highways in any state that did not raise the age to 21. The law was upheld by the U.S. Supreme Court in the South Dakota v. Dole case. Congress was not allowed to change the drinking age directly because the 21st Amendment (which ended Prohibition in the U.S.) gave control of alcohol to the states. In 2009, Congress considered similar legislation regarding texting while driving.

   This power was curtailed somewhat in a case regarding the Affordable Care Act, in which the Supreme Court ruled in June 2012 that the law's withholding of all existing Medicaid funding for states that failed or refused to expand their Medicaid programs to cover the uninsured poor was "unduly coercive", despite the fact that the federal government would pay the entirety of the states' expansion for the first years, and 90% thereafter. It was left unclear what percentage would be considered acceptable.

2. Separation of powers across branches. The Constitution only hands out certain authorities to the Executive Branch. Within the Executive Branch, the President has a pretty free hand, but only within that.

One major benefit Trump has right now is that Congress generally is onboard with what he's doing -- the Republican Party holds a trifecta, control of all three of the Presidency, House, and Senate, so a lot of the restrictions that a President might normally face aren't really there unless he does something that his own party really doesn't like. The common case is that the "other" party has control of at least one, so can usually block a lot of actions.

3. Some actions by the federal government are simply prohibited by the Constitution.

But the federal regulations, including auto safety standards...those are federal and in the province of the Executive Branch, so if Trump wants to have them changed, he probably can do it unless some change actually violates the Constitution. If the President wants to listen to Some Random Person, like Musk, as to what to do, he can do that too.