Phase noise in spectrum analyzers
For your first question, it's necessary to distinguish between long-term and short-term frequency jitter. If the frequency is off by a fixed amount, and this offset changes slowly, then the peak in amplitude on the display will be displaced in frequency by that amount. If on the other hand the frequency changes back and forth extremely fast (short-term frequency jitter), this is similar to FM modulation, and shows up as phase noise. This short-term frequency jitter (as opposed to long-term frequency error) creates the noise "skirt" referred to in the application note.

For your second question, there is usually a given amount of phase noise for a given bandwidth: phase noise is expressed in units of dBc per Hz of bandwidth (dBc/Hz) at a given offset. This amount is not fixed, but varies depending on how away from the carrier you measure the noise. Nonetheless, as the bandwidth of measurement increases, the total noise within that bandwidth also increases. Thus if you set the RBW filter wider, then it is integrating and averaging noise over a wider bandwidth. If you set the RBW filter narrower, then it only picks up the noise over that narrower bandwidth.