A Primer on United States Treasuries

There are several other key points relating to treasuries (and nominal rates in general) which haven't made it into your article, but are probably more important than anything you've mentioned:

• Correlation with the real economy
• Inflation (aka nominal vs real rates aka UST vs TIPS)
• Hedging properties of treasuries

There is a general thread running through this whole article whereby you are alternating between "Treasuries" and "Risk-free rates". Given that treasuries are considered the risk-free rate, there's a degree to which mixing these things up "doesn't matter". Contrary to this, I think it is important to distinguish between these things, especially when talking about how these things relate to other assets.

Roughly speaking, there are two ways in which the risk-free rate affects pricing of other securities:

• As an arbitrage bound / discount rate for pricing things in the future
• As an "alternative" in an investment portfolio

(I associate the first one more with RFR and the latter more with treasuries)

Most of your examples are in reference to RFR. (In fact, everything you wrote could be replaced with "everything is discounted using DCF and the discount factors come from Treasury prices" (which somewhat misses the point that treasuries are priced via DCF...))

FX

The key question here is "which fx rate moves". (Ie Forward rate vs Spot rates). The forward rate for an FX pair is defined by an arbitrage bound. (Actually there is much more which could be said about this relating to cross-currency basis, but this is not the place for that). The forward exchange rate (how many EUR can I buy with 100 USD in a years time) is defined by an arbitrage. I can either buy my EUR today and put them in a EUR bank account, or I can put my USD in a USD bank account today and exchange them for EUR in a year. If EUR rates are -50bps and USD rates are 0bps, then I will have either current_exchange_rate * .995 in a years time or forward_exchange_rate * 1 in a years time. These two values must be equal (otherwise there's an arbitrage), so the forward exchange rate is fully determined by the differential interest rate in the two countries.

Now if interest rates go up in the US, then dollars vs euros today needs to move OR dollars vs euros in a years time needs to move.

This is [mostly] an arbitrage relationship rather than anything to do with USTs as an asset class.

There is a level on which these things are more complicated. mostly driven by the action of large foreign investors who typically have a maturity mismatch between their bonds (often long bonds) and FX hedges (often 3m-1y rolling). This generally means that spot rates bear the brunt of the moves.

Corporate Bonds

What you've written is technically true. (Although you could re-write the whole paragraph replacing "corporate bonds" with "US treasuries" and convey as much information).

This is [kinda] an "alternative" example. If I'm choosing between lending my money to the US Government and Acme Corp, then I expect to earn a rate slightly higher than if I lend my $ to the government.

When thinking about corporate bonds (at least higher rated ones) the important bit is (as you say) the credit spread. The more interesting question is "how does the credit spread relate to interest rates". In general, they are positively correlated, because as interest rates go up, their credit burden goes up, so their creditworthiness goes down (and vice versa). [There's some complications in all of this but lets leave aside for now]

Fixed Rate Mortgages and other Fixed Rate Loans

US fixed rate mortgages are a messy product. To first order, what you're saying is true, but only in the same sense as everything else. "Everything is discounted using DCF and the discount factors somehow come from treasuries". (Which is pretty circular).

Equities

That chart is a chart-crime on so many levels.

One of the most common ways to value a company is The Discounted Cash Flow Model. One of the inputs of the model is the discount rate. The higher the UST rate, the higher the discount rate. The higher the discount rate, the lower the present value of the company according to the model.

This misses the woods for the trees. Why do we use DCF? Because of alternatives. If a company is offering me $100 in cashflow in a years time, how much should I be willing to pay for that? Well, a decent starting point is "how much can I buy that (future) $100 from the government for. So another way of saying the same thing is: "If the return on owning treasuries increases (ie bond prices down, rates up) then the return on owning equities should increase (since people can get the a better return elsewhere otherwise)".

Relatedly, you might find Fight The Fed (Asness) interesting.

Commodities, Futures, Options

Pretty much all of these fall squarely in the "risk-free rate as arbitrage" camp. (At least to a first order approximation). 

Some important nitpicks:

One of the most common UST is the UST 10 year bond.

I'm not sure what you mean by "common" here. Some senses in which the 10y isn't the "most common": 

• Not the highest outstanding notionals
• Not the weighted average maturity (or duration) of the whole stock
• Not the highest volume traded (either by notional or duration (or as a derivative))

I'm guessing you mean something like "most commonly cited by the financial media".

You can buy treasuries that mature in most months and many different years, but only a select few are tracked by the markets, and are the reference rates that are used by the markets to drive expectations and investment decisions.

Err... what? I'm not even sure what you're trying to say? Perhaps you mean something like: "A few benchmark points are observed more closely", but generally people making investment decisions will just take the whole yield curve. Or perhaps you mean "The US only issues bonds at a certain subset of durations"? Not really clear to me.

All else being equal, when USTs are rising across the board, it means that the United States dollar will strengthen, assuming that rates in the foreign currency in question are stable or dropping

This is a massive problem people have when talking about bonds. USTs are treasury bonds not treasury bond rates.  When USTs are rising, rates are falling. Here you mean something like "When USTs sell-off / fall and US rates rise ...".