What's going on with sudden acceleration/deceleration in mid-air?
Without knowing the specifics of the flight, there could be a lot of reasons for this.

One guess for the sensation of accelerating and decelerating We’re intermittent steps at fixes on the departure procedure the pilot flew out of KLGB at certain altitudes and airspeed either as part of the DP or as assigned by ATC in order to facilitate departure from SoCal airspace to enroute.  That and a little sloppy airmanship on the part of the flight crew.

As for the “circling” at KPHX,  most likely that was the pilot flying a STAR with ATC final vectoring to a visual approach or SIAP for runways 25L/25R/26 at Sky Harbor Intl.