You can't compare the analyzer's RF noise floor with no signal applied (in the last screenshot) with its phase noise floor, which might be showing up in the other screenshots where a carrier is actually present.
Also, see if there's a noise marker feature you can use (note that the Agilent screenshots are showing marker values in dB/Hz, not dBm). If no noise marker is available, you will need to subtract 10*log10(RBW) from any marker readings to normalize them to a 1 Hz bandwidth, and also subtract the carrier amplitude if it's above 0 dBm. This will be valid to within a dB or two,
if the noise you're measuring is well above the analyzer's LO noise floor.
The spurs look like some type of modulation is enabled. Either that, or there's a problem with the analyzer or the signal generator.
The 8600A series analyzers are supported by my freeware
phase noise app, which can automate some of the number crunching for you if you have a GPIB adapter. I don't have any baseline data for the 8609A but I do have a baseline plot for the 8604A, and it's not exactly one of the all-time greats:

Chances are that the Erasynth Micro unit is quieter than this particular spectrum analyzer model, unless the 8609A is significantly better than the 8604A. I've never actually had my hands on one of them in person (either the synthesizer or the 8600A-series analyzers.)