# Amplitude of gravitational waves at emission and how they decay

I am a bit confused with some aspects of gravitational waves (GW). GW we observe here on Earth with LIGO/Virgo have an amplitude of $$\approx 10^{-21}$$ with peak frequency $$\nu = 150\, Hz$$. If we assume that the strain from two black holes with same mass merging goes as \begin{align} h &\approx 2\frac{GM}{c^2}*\frac{1}{r}*\left(\frac{v}{c}\right)^2 \\ &\approx 3 \times 10^{4} m * 10^{-25} m^{-1} * (0.25)^2 \\ &\approx 2 \times 10^{-22} \;, \end{align} we obtain a pretty good approximation. What I want to know is:

1. since GW decay as 1/r, can we assume that the amplitude at emission $$h_{em}$$ is roughly obtained assuming $$r=2GM/c^2$$ (i.e. produced near the Schwarzschild radius of the final BH), so that \begin{align} h_{em} &\approx \left(\frac{v}{c}\right)^2 \\ &\approx 10^{-2} \;? \end{align}
2. GW decay should also depend on time (as hinted, for example, here). But after spending a few hours looking in the literature, I haven't found any derivation showing both time and distance decays of the strain. Does anyone have references on the subject?
3. the physical process leading to astrophysical GW is much less energetic than, say, inflation. So, when we say primordial GW (PGW) are harder to detect, is it only due to the decay with distance (and/or time) that is much greater?
4. The period of an astrophysical GW depends on the radius R of the orbit as $$T_{GW}=2\pi R/\nu$$. This formula does not make sense for PGW. Is there a way to obtain the period of a PGW?

Cheers!