Air carrier crew reported a conflict with another aircraft while landing. The Captain identified the other aircraft taking off on the crossing runway and braked hard on landing rollout to remain short of the conflicting aircraft.

Reporter 1

Maintenance write up just short of takeoff runway for seats not staying. PF/FO (Pilot Flying/First Officer) pushed through TOGA on takeoff roll as they did not feel the AT (Autothrottles) grab the throttles. It took me a moment to realize why we were above thrust and by then I elected to continue and maintain thrust until airborne. Once airborne, I corrected thrust and reengaged the autothrottles. We were then given a climb to 7000 which was immediately changed to 6000 at about 5500ft. This caused an altitude deviation up to 6200 ft which we then corrected. The remainder of the flight went well and we discussed what had occurred and why. On landing, we were given cleared to land [Runway] 15R/09. The PF (Pilot Flying) landed correctly and applied reverse thrust, and tower gave the aircraft on [Runway] 27 clearance for takeoff. I noticed an aircraft moving forward on [Runway] 22L approaching the intersection 15R/22L with their lights on and called out maximum braking. I simultaneously took the controls and applied max reverse thrust and braking, stopping short of 22L. We taxied into the gate with no further issues. I filled out a report and noticed I had never sent the response to accept the amendment for adding the MEL when reviewing the messages. I called dispatch and the dispatcher confirmed they never received an affirmative response to the amendment over ACARs. Suggestions: For taking off without the amendment, I need to go a bit slower and be sure I comply. I counseled the FO to not push through the detent on takeoff (it was the first time I’ve seen it done) and to push them up slowly so the AT has a chance to grab. For the altitude deviation I counseled the FO to fly the plane first, overriding as necessary and then we can check the modes and to not be over-reliant on the automation.

Reporter 2

Taxied out to runway XX flight attendants called up stating an issue with the seat back. We pulled to the deice pad and wrote up the issue. Then applied a crew applied MEL for the issue. After completing those paperwork items we taxied to the runway we were given a takeoff clearance with an aircraft on a 4 mile final on the other runway. The captain pulled the aircraft onto the runway with engines spooled. I then took the trust levers and flight controls. I continued the advancement of the throttles and accidentally went past TOGA. The pilot monitoring noticed the issue and corrected the issue. We cleaned the airplane up and engaged automation. However at approximately 5,500 feet we were given a level at 6,000 feet when originally given 7,000 and a direct to a fix. I dialed in the altitude to make sure it was set at 6,000 before the aircraft was above that altitude. Instead of watching the level off to ensure the automation did it correctly I went into the box to get the aircraft flying direct to the fix and the aircraft went to around 6200 feet before leveling at 6000. Also, we were given an altitude at cruise where the controller mentioned if we were starting down to that altitude and we had not yet and he instructed to start the descent at that point which we complied with. On landing we were given a hold short of runway 9. The touchdown was uneventful and I applied braking and reverse to comply with the hold sort of runway 9. Shortly after that the captain join the controls and said my controls. He braked heavily and stopped the aircraft. Further stating that the piston Cessna on 22L appeared to move and we stopped just short of 22L. We then taxied off clear of the runway and continued taxiing uneventfully to the gate. Suggestions: Not letting things compound starting with the maintenance issue than the takeoff clearance where I should have taken my time after reading back the takeoff clearance before receiving control and taken more time during throttle advancement to ensure it was done smoothly and does not exceed TOGA. Also, to pay closer attention to altitude clearances and closer attention to the automation to ensure the aircraft meets the altitude clearances without deviation from those clearances.