Electrical Engineer here, that corrosion doesn’t look too bad, I wouldn’t assume it’s the issue but it’s not impossible it might be a contributing factor since corrosion on connections can cause heat and heat can trip breakers.

If the breaker trips are happening when you do something like turn on the oven or the toaster then it’s just a matter of the electric service to the house being too small for the apartments loads. This can happen if the apartment originally had gas appliances that were later switched to electric or something else (like a hot tub) was later added to increase the electric load beyond what was originally designed for.

If the trips dont seem to correspond to anything you’re doing with electric appliances, then the equipment may be going bad or there may be an intermittent short. Both of which are not something you would be able to troubleshoot (and frankly, if you don’t know what you’re doing, even opening up a panelboard like you’ve done can be deadly).

Either way I highly recommend you either pressure your landlord to bring in an electrician, or pay for one out of pocket if thats not an option.