Just bought a small remodeled home in March which has all new wiring and new inside breaker panel with all combination gfci/afci circuit breakers. The microwave breaker would occasionally trip over last few months. Suddenly the kitchen breaker tripped over night when the robotic liter box (it's not new) was running. Plugged litter box into living room, that breaker tripped. Unpluged litter box. Then later all lights in the home started flickering and continued to do so sporadically. I could hear crackling at the outside main breaker panel. Called CPS and they replaced the wire from the pole to the house. Then I hired someone who swapped out 4 inside breakers (kitchen lights, living room, smoke detectors, microwave) for standard breakers under the advice that afci/gfci breakers "are too sensitive for appliances" and things seemed fine. Litter box has not tripped breaker nor has the microwave. Then the lights started flickering again a few hours later. This morning the bedroom 2 breaker tripped and all lights were flickering. The only thing on in bedroom 2 was an iron which I had just plugged in. I have not had any issues with the washer/dryer nor a/c but they have their own main breakers on the outside main breaker panel. Any ideas what might be happening?

Okay you have quite a bit going on here. Let's start with the oldest major event. I'm guessing that CPS is your electric utility company. You said you heard "crackling" at the outside "Main Breaker Panel" (?) Does this mean the panel where the overhead electrical wire connects to the meter? If so, does the panel that holds the meter also contain circuit breakers that service circuits on the inside of your home? Or does the outside meter panel feed the inside panel box that is giving you trouble? This is a very important question.

Also, when the utility company changed out the overhead cable, did they also change out the meter base or tell you that the meter base needs to be replaced? Also an important question. At this point I suspect that one of the meter base lugs is bad which will cause a clicking sound when it heats-up and loses connection. You might want to call the utility company back and have them make sure that their wires and equipment is correctly installed.

With respect to the new wiring, do you know whether or no a licensed electrician did the work and if so, was the electrical wiring inspected at the completion of the work?

Now to the nasty stuff. Current electrical code requires the AFCI and GFCI protection be installed. AFCI protects against fire by watching for electrical arcs. GFCI protects people against electrocution. Neither should be removed because it causes problems with appliances. That's called nuisance tripping.

Some things to look for, particularly in the kitchen. The electrical code requires two 20 amp branch circuits to serve counter top receptacles. Sometimes in a effort to reduce costs, a "Multiwire Branch Circuit" is installed. This is perfectly allowable, if it is installed correctly. If it is not, it is a nightmare waiting to happen.

A multiwire branch circuit shares a common Neutral (White) between two circuit breakers. If that Neutral is not shared (connected) properly and one Neutral connection becomes loose you will end up putting 240 volts across a device, such as the litter robot, and correspondingly high amperage. If the breaker is quick enough to catch it you are fine, however, if it is not anything else downstream of that connection could fry.

Lastly, lights are normally are on 15 amp circuits and should never be connected to the counter appliance circuits.

I think you need to find an electrician who is qualified and has experience with troubleshooting arc fault problems. Find someone with a little grey hair with a commercial / industrial background and good luck...