What checks and balances exist on executive orders? What limits?
In an ideal world where the US government is working correctly, US executive orders are limited by the Constitutional powers of the Presidency. That is, the President doesn't write laws, doesn't set taxes, and doesn't set budgets because those are powers reserved for Congress. Accordingly, executive orders cannot create new laws and taxes, and can't change budgets issued by Congress (with caveats - a vague budget for a federal department gives a President a lot of leeway).
Further, executive orders are subject to judicial review just like Congressional laws. The Supreme Court can invalidate an executive order just like it can declare a new law to be unconstitutional.
The US President is basically a chief executive for the US federal government's bureaucracy. Presidents' job is to execute the laws and budgets set by Congress. Executive orders are thus directives from the boss to employees in the federal bureaucracies and must fit within existing laws and budgets.
To put it another way, executive orders should try to clarify or help implement laws, not make laws.
Some example executive orders:
George Washington cut the first executive order and it was a 1789 directive to heads of bureaucratic departments to (in so many words) "Tell me what's happening in your department." With that order, executive departments got a new rule to start keeping their boss informed of events. It seems like a fairly obvious order but apparently the new federal government was a bit haphazard and didn't have any prior written requirements for the new departments to tell their boss what they were doing.
President Lincoln's "Executive Order Establishing a Provisional Court in Louisiana" (1862) would normally have been completely outside a President's powers since the judicial branch handles the courts. However, Louisiana was in rebellion, had been captured by federal troops, and was under martial law. Presidents being the head of the US military, it was within Lincoln's wartime powers to set up courts to restore order in Louisiana. These courts ended when Louisiana returned to civil administration.
One of the most famous executive orders came from Lincoln and was again applied to rebellious states only: the Emancipation Proclamation. The constitutionality of freeing slaves elsewhere might've prompted a serious court fight over an executive order or even a Congressional law, hence the US eventually had to amend the Constitution to eliminate slavery.
On the other hand, Harry Truman's Executive Order 10340 attempted to federalize all US steel mills ahead of a disastrous strike and was slapped down by the Supreme Court. The reason for the decision was that this executive order attempted to make law, which is a power reserved to Congress, rather than to "clarify or further a law put forth by Congress."
Since that 1952 defeat, executive orders have been written to carefully cite laws or fundamental Presidential powers in the Constitution that allow the orders to work.
Clear as mud? :)
I'm not sure what existing laws give the President authority to shutdown specific websites, so I can't comment on the TikTok matter.