Why does lowering stock rate of returns increase stock prices? (i) I don't understand point 1 beneath. Why does the Federal Reserve's buying assets lower risk premiums?

(ii) I don't understand point 3 beneath. Why does lower stock rate of returns increase stock prices? Won't lower stock rate of returns lower stock demand? Won't some investors buy something else other than stocks?  

Why the stock market is going up... and it's not because the Coronavirus is going away : investing


  I think I know why the stock market is up... and it's not because the Coronavirus is going away.
  
  It requires some macroeconomic and finance knowledge, but maybe, just maybe:
  
  
  Fed actions (buying assets) are lowering risk premiums
  Fed actions (lowering rates) are lowering asset yields overall
  Both of these actions lower stock yields, which increases stock prices
  Lower stock yields = longer duration for stocks (dividend discount model)
  Longer duration + lower stock yields = less overall sensitivity to the lower expected earnings for next 12-24 months due to Coronavirus
  Plus... a maybe.... maybe long-term inflation expectations due to printing money = higher earnings (in pure dollar terms) for cash flows 5-30 years from now
  
  
  Run those things through a discounted cash-flow model, and you get higher stock prices. Near-term earnings become less important to the overall picture.
In the part 1 there must be some omission. Just by itself a random Fed purchase would not reduce risk premiums. However, a targeted Fed purchase can reduce risk premium as non-trivial part of risk in any firm stems from liquidity risk. Through purchasing assets of illiquid firms Fed can provide them with liquidity that they need and thereby reducing the risk that they fail just due to illiquidity. Also as Fizz points out in his comment this is just one example, there are several other channels that can also lead to risk reduction as well.

The intuition behind this is that the stock prices represent present value of the future expected income streams you get from the stock and at lower interest rate the present value of this income stream becomes higher. To see why this makes sense consider practical example where the stock always pays dividend 10\$ in perpetuity. Then in order to actually calculate whats the present value of getting the stream of 10\$ at 10% you can use the Gordon formula which is just based on calculating the value of infinite sum. In simple Gordon stock pricing formula given as $P=\frac{D}{r-g}$ where $D$ is dividend and $r$ rate of interest and $g$ rate of growth which we can for sake of simplicity ignore and assume its zero so we get $P = \frac{D}{r}$.
At the 10% the infinite sum of 10\$ will be worth 100\$ because
although your are getting the dividend in perpetuity due to time
value of money money in future is less valuable than money now and
becomes less value the more you look into the future and hence this
infinite sum in present value terms becomes smaller and smaller
which allows us to actually calculate finite value even for an infinite stream of money. However, now if the interest rate drops to 1% the present value of those dividend streams becomes higher and the stock will now cost 1000\$ as now the future is discounted less heavily. To put it simply, at lower interest rate the money you receive in future have higher value today.