Hello Chilangopolaco:
It looks like you have Masonite siding there. It has a tendency to go back to its natural state when confronted with weather. It is made of sawdust and turns back into it.
It looks like you have done a nice job of replacement and yes, you could cove the joints with 1 X 4 for a neat appearance. Meanwhile you need to be thinking and saving for the day when you will replace the whole thing.
Glenn
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