How is channel frequency response/channel state information related to free space path loss? As we know, the path loss can be described by the equation as
$$
\frac{P_{r}}{P_{t}}=D_{t} D_{r}\left(\frac{\lambda}{4 \pi d}\right)^{2}
$$
In the OFDM system, such as Wi-Fi, there are infinite paths exist, assume it is in free space, and only one path exist, for the specific path (LoS path), the channel frequency response(CFR)/channel state information(CSI) describes how is the channel affect the transmitted signal, it calculated by:
$$
H = \frac{Y}{X}
$$
where Y is the received signal at receiver and X is the transmitted signal at transmitter. the signal power is square of the amplitude of the signal, that is
$$
P_{t}=|Y|^2
$$
$$
P_{r}=|X|^2
$$
I have two questions:

Is the following equation holds?
$$
\left|H_{}\right|^{2} = \frac{P_{r}}{P_{t}}=D_{t} D_{r}\left(\frac{\lambda}{4 \pi d}\right)^{2}
$$
According to the first equation, is the following equation holds?
$$
\frac{X}{Y}=\sqrt{D_{t} D_{r}\left(\frac{\lambda}{4 \pi d}\right)^{2}}
$$

Thanks in advance.
In the OFDM system, such as Wi-Fi, there are infinite paths exist, assume it is in free space, and only one path exist,

Exactly. So if you use OFDM in a scenario where FSPL describes your transmission sufficiently, then you're doing something wrong, because you don't need OFDM, as you have a flat channel.
We can still describe large scale fading in multipath channels using models similar to your FSPL formula, but neither of your equations hold! Then, we're describing distance-dependent stochastic properties of the random variables that make up your CSI.
You need to cross over from your deterministic &quot;this channel has a defined attenuation&quot; model to a stochastic &quot;and here's how we describe the properties of random variable, whose realizations are channels&quot;.