Strange TX spikes 20m

This is normal - nothing to be concerned about.  Your radio meets all requirements for spectral purity on transmit. You are seeing a very low level artifact in the that is generated internally in the radio and NOT transmitted.  Note that the signal level is around -130 dBm (as best as I can tell).

Also, in the 20m test, you had left the RF Preamp on and that was what was causing some of the display "spikiness".

In FlexRadio support, there is a saying we have since the first panadapter was coded in PowerSDR, many moons ago; "the best thing about the radio is the panadapter and the worst thing about the radio is the panadapter",  This comes from the fact that now you can see RF artifacts, birdies, noise and other RF stuff that had always been there with other radios, but now you can actually see it with an SDR.

We debated about blanking or deliberately modifying the display to hide the low level symmetric side band signal peaks on transmit and in the end decided it was best to show the spectrum as it is on transmit than to do anything artificial.

There is one other key difference in the two panadapters that is subtle.  On 20m you have the panadapter Weighted Average function turned on.  This favors the peaks in the panadapter and causes a drastically different look for the same data.  Try turning this off and comparing also.  I wrote a more detailed explanation of this function in this post:

https://community.flexradio.com/flexradio/topics/weighted-average

Gerald explained the low-level spurs seen in the receive panadapter during transmit here:

https://community.flexradio.com/flexradio/topics/panadapter_spurs_in_tune_mode

In general, the receive pattern of the transmitted waveform is useful to see, but do not look too closely at any spurs out of the local transmit filter.  In almost every case these are caused by the proximity of the receiver and transmitter in the radio and are not actually being transmitted.