For comparison here's my SPL (1/24 smoothing), waterfall and spectrogram for my right speaker:



The spectrogram clearly shows that at 30-50Hz and at 80Hz the noise is heard before the REW signal is made - the signal is made around zero seconds yet there is noise before that in the minus milliseconds. This noise continues so it is not easy to know how the REW signal decays in this region. This is external noise from traffic. You can also see this on the waterfall plot. I made a measurement on Christmas Day and I didn't get this response.
It's odd that your spectrogram has noise all the way through the frequencies before the REW signal. I don't know what that means unless you have some background noise going on. You can find out by measuring with your microphone without playing the REW signal.
My waterfall plot has a range of 37dB above the noise floor. Yours seems to have about 28dB (a rough average of the lowest dBs (60dB) taken from a rough average of the highest dBs 88dB)). I was told that waterfall plots are not much use above around 500Hz.
For the 1/24 SPL reading you could use the 'control' button on REW to adjust the scale, say to between 75 and 90dB and 20Hz to 20,000Hz. It won't look so smooth but will be more informative. Yours seems to have a range of around 11dB which seems pretty good in comparison with mine of about 17dB excluding the traffic noise.