Calculating SNR from Frequency-time domain
This is probably not going a particularly satisfactory or useful answer for you. SNR is a ubiquitous concept in Signal Processing and one would expect a correct straightforward calculation on data would be available and it basically is:
$$
SNR=\frac{\text{Signal Power or Energy}}{\text{Noise Power or Energy}} 
$$
so you just look at your spectra and identify the signal and noise and make the calculations. This is usually straightforward to do theoretically. In some applications these identifications are easy and in others less so and looking at your data, not much looks obvious. A FFT of the data didn't make what is signal or noise obvious to me and if were obvious to you, you probably would not be asking so 
$$
\text{Correct} \;SNR \ne \frac{\text{Hard to tell Signal Power or Energy}}{\text{Hard to tell Noise Power or Energy}}. 
$$

Instead, 
$$
\text{Plausible} \;SNR = \frac{\text{Plausible Signal Power or Energy}}{\text{Plausible Noise Power or Energy}}. 
$$
is likely to be more successful. I've actually had to present these issues to management and at the end been asked if this was "correct". Saying yes has usually been the "correct" answer.

Getting back to you data, the frequency time graph has some quiet spots that are probably your best candidates for a plausible noise estimate.  This assumes, that the noise is stationary, but looking at everything else in the time frequency plot, this seems plausible. Extract a Noise Power estimate from the quiet segments and average as many as possible. Also I'm guessing that the signals are of finite duration.
$$
\text{Plausible} \;(S+N)R = \frac{\int_T (\text{Plausible Signal + Noise Power}) \; dt}{\text{Plausible Noise}\times T}. 
$$ 
where $T$ is the signal duration.  

Some details, We have Parseval's Identity,
$$
\sum_{n=0}^{N-1} x[n] = \frac{1}{N}\sum_{k=0}^{N-1} \mid X[k] \mid ^2$$
and the variance of a sum of $N$ independent random variables
$$
\sigma^2_{\text{Total}}= \sum _{k=0}^{N} \sigma_k^2.
$$
The random variables don't have to be Gaussian, they just need to have a variance.

For long DFT's noise bins are approximately independent, summing the noise power present in each bin is a reasonably same assumption if the noise is approximately flat across the spectrum.

If your signal is known, the energy can be calculated using Parseval's Identity.  If your signal has random characteristics, The signal bins are probably not independent and summing bin power may not be the best plausible method.  If you have enough data, you can estimate the covariance 
$$
Pwr=\mathbf{x}_{sig}^H \mathbf{R}\mathbf{x}_{sig}
$$
which is a power quantity.

For complicated signal and noise scenarios the most reasonable method is to derive a model, not necessarily a full model, and simulate your SNR estimation process.  

The answer to 50 is a heuristic to account foe signal leakage outside the nominal signal limits.

Two issues with your question

The time frequency plot indicates frequencies to 1MHz but your spectrum is 500KHz.  You really should know why.

Using Unix time as a time index is terrible.  You make the reader work.  

Most of this didn't really give you the answer you were looking for.  There is no straightforward fully general way to calculate SNR without knowing what is signal and what is noise to a high degree of specificity.