Date: 202103
Local time of day: 0601-1200
Location: ZLA.ARTCC, CA
Light: Daylight
Aircraft: EMB ERJ 135 ER/LR
Operator: Air Taxi
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class A ZLA
ATC / advisory: Center ZLA
Second aircraft: Any Unknown or Unlisted Aircraft Manufacturer
Reporter organization: Air Taxi
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Human factors: Situational Awareness
Second reporter function: First Officer; Pilot Flying
Anomaly: Conflict Airborne Conflict; Inflight Event / Encounter CFTT / CFIT
Detector: Automation Aircraft Terrain Warning; Automation Aircraft RA
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Flying from ZZZ-BUR we were in cruise assigned by ATC to start a descent from FL220 to FL180. Upon passing through FL215 ATC asked us to stop our descent at FL210; we complied and stopped at 210. Upon reaching 210 we received a TCAS TA. The FO and myself immediately looked at the TCAS screen and started to visually look for the traffic. He was getting closer to our six mile ring and he was still climbing; we saw him on our TCAS inside of our six mile ring and now at our same altitude. It was at this time the we received an RA. The FO immediately disconnected the autopilot and started to comply with the RA. At this time ATC told us to climb to FL230 I told him we were complying with an RA event and we could be unable to climb to 230. The RA initially gave us a command to descend at 3200 FPM and then the rate of descent was increased by the RA to 4500 FPM which was complied with. We leveled the aircraft off after the RA was complete at FL190. We asked ATC if he had any further instructions for us; he said to level at 190 and he would be back momentarily. He proceeded to give the other aircraft that caused the RA a phone number to contact center. The pilot sounded like he was possibly in distress in a potentially hypoxic situation from the tone and behavior of his radio calls and struggle to follow any ATC instructions at the time. We continued to descend into Burbank and now on SoCal Approach were given a heading of 150 and 5k feet which took us right over a mountain that gave us a terrain warning momentarily as we leveled at 5k feet. We cross this terrain at 5;000 often on a vector from ATC we happened to cross right over the very peak of this terrain and with the descent rate down we suspect that the rate of closure was too much for the GPWS.  Upon landing in Burbank on the ILS Z 8 we received on more TCAS TA/RA as we crossed over ZZZ1 traffic in the pattern below caused our TCAS to give us a 'Monitor vertical speed' we complied and landed at Burbank without further incident.All events that took place were as a result of other aircraft and ATC vectors. We as a crew exercised all appropriate training to comply with all events.


Second narrative: While operating ZZZ-BUR level at FL 220; LA center on 132.5; issued a descend and maintain from FL220 to FL190. Passing through FL21.5 ATC amended clearance with a limit of FL210. We leveled off at 210 without any deviation but noticed an aircraft rapidly approaching our guarded zone on TCAS. Momentarily after we noticed this; a traffic advisory was made by the TCAS system and followed by and immediate command for 'monitor vertical speed'. The vertical speed initially commanded was 3700 fpm. The target aircraft did not level off at their assigned altitude. After the autopilot was immediately disengaged and the descent was initiated to the commanded rate; the TCAS prompted 'increase vertical speed' commanding roughly a 4500 FPM decent rate. LA center was notified and after the aural clear of conflict was heard and agreed on the aircraft was level at FL190 and ATC issued a new clearance. With no further issues the flight continued through Joshua approach and then onto SoCal approach.  With SoCal approach upon completion of the JANNY5 arrival into BUR SoCal assigned a vector of hdg 190 and descend to 5;000 ft. Level at 5;000 feet we crossed over a mountain peak that was at 3;734 feet. This caused a terrain warning and a subsequent ' terrain terrain pull up'. The aircraft climbed roughly 100 ft since the conditions were VFR and clear. After the terrain clearance was accomplished; SoCal assigned a heading of 110 and 3000 till established and cleared for the ILS-z Runway 8 into BUR. Upon passing over ZZZ1 we received another traffic advisory and that was followed with a RA. The RA did not state any vertical speed as the target aircraft had already passed behind us. The flight landed at BUR on Runway 8 with no adverse issues or events after that point.Continue to follow SOPs and be a vigilante and proactive flight crew and practice good CRM techniques.


Synopsis: Air carrier flight crew reported that during arrival into BUR airport they had experienced an RA and later had a terrain warning caused by passing over a mountain peak at a high rate of descent.