For the two panels in series, the voltage doubles and the amperage stays the same. For example two 25 volt panels at 4 amps in series would produce a 50 volt at 4 amp output. When two additional series connected panels are added in parallel, the voltage will remain the same and the amperage will double. With the four panels in this example in series parallel (2S2P), the end voltage will be 50 volts and the end amperage will be 8 amps.
I am not a fan of the in line fuses like you found on your set up for the reasons your system is having issues. They tend to blow at very inconvenient times. Most that I have found are typically installed incorrectly as well. They tend to be installed in the wrong place in the string and end up getting more amperage than they are rated for as a result and blow. I had to remove one from someone’s system the other day for this exact reason. It was installed in the wrong place in the array and was getting more amps than it was rated for.
I prefer a DC rated breaker down by the solar controller. Not so much for the circuit protection ( for the reasons Lou Schneider explained), but to be used as a shut off when I want to isolate the panels from the system for testing or service or whatever. Plus a circuit breaker is resettable rather than having to replace a fuse.