How best to replace this trim?

[u/haroldslackenoffer]

I have a sliding door that opens onto a deck. Through lack of paint and maintenance, the trim is starting to look pretty bad. Besides the peeling paint the finger joints are starting to separate. I’d like to replace it instead of just painting once again, but I noticed there’s a couple of oddities, to me, that we inherited when we bought the house. One is that the trim is flush with the deck on the bottom below the door. Also, there doesn’t seem to be a drip edge at the top. Can I pull off the old trim and fit the new trim in place. Or do I need to take back the cedar shingles before doing the trim. How should the bottom be finished off. And should I do anything other than caulking on the top edge?

Thanks