Does treasury pay interest+ face value to the fed?

Yes, Fed sends all its profit including the ones it earns on government debt back to the treasury (this was already answered on this site here). Fed can create an unlimited amount of money by buying treasuries but not because of the interest payments but because of the debt itself.

The interest payments themselves do not generate new money in this relationship when they are paid back to the treasury, that is just juggling money around. Government, has to pay interest on its bonds and through the transfer of the profits from the Fed to the treasury any interest government paid is sent back. So for example, if the government pays ${$}100$ interest payment to Fed, Fed's interest revenue will be ${$}100$ higher. Fed has mostly fixed costs, variable costs associated with processing extra interest payments are small so we can reasonably assume that in this case their net profit also increases by ${$}100$ and hence this money will just make a full circle from the treasury through fed back to the treasury. So the interest itself does not generate new money.

However, when Fed purchases a bond from the government it actually can do that with newly created money. That money will exist until government decides to repay the face value of the bond and Fed could just let that money exist by simply 'scrapping' the bond itself.

Through creation of new money, this way Fed and government in general is able to generate some real revenue - this is called 'seigniorage'. However, only limited amount of real revenue can be created this way. Empirical studies show that most countries including US have seigniorage revenues around $1-2%$ of GDP (see Haslag's Dalas Fed brief on this). That is not entirely non-trivial but also not much compared to other revenue sources.

The reason why government cannot just create unlimited ‘profits’ for itself this way is that, in economics, there is a strong consensus among top economists that only a limited amount of real spending can be financed through money creation. This is because creating more money (aside from special circumstances as when economy is at zero lower bound) is generally inflationary which means that although you created new money they are also worth less - have lower real purchasing power (see textbooks like Blanchard et al. Macroeconomics; Mankiw Macroeconomics etc.). The government can still earn little bit of extra revenue from this, but even if it can in principle create an unlimited amount of money that does not mean it can also purchase an unlimited amount of goods and services.

There’s already a longer answer, but two points of clarification.

1. The Treasury would not “make money,” it just gets the interest back.
2. The Fed purchases create settlement balances (“reserves”) for banks. (The Fed is a bank itself, those balances are the equivalent of private banks leaving deposits.) The Fed pays interest on those balances. When they need to hike rates (presumably to reduce inflation), they need to correspondingly increase the rate they pay on those balances. This reduces the profit for the Fed, and if the paid interest rose higher than their coupon income, the Fed would lose money. (This is the longer explanation of the remarks by 1muflon1 about the zero lower bound.) As a result, this would not be considered a risk-free profit opportunity for the government.