I have a few questions on where to find various records for a person I'm trying to get information on. I'm trying to trace my great grandfather's Moniz (possibly Cordeiro) line and I have an Ancestry DNA match to someone who does not match to people in my great grand mother's line. I'm hoping that this person may hold some clues to my Moniz ancestors. Unfortunately my match's tree is not built out past the below info so I'm trying to do some work here.
The oldest record he has is the birth and baptism of a Manuel Moniz in Hawaii in 1898 (see below). I'm trying to get info on his parents Francisco Moniz and Maria Rosario Resentes, however I cannot find Manuel's birth record or Francisco and Maria's immigration records, and I can't find them in the census.

I'm familiar with where to find the Azores passport and baptismal record images, but where are the images for Madeira? I used the search tool but I'm not seeing where to go to so I can find the relevant passport record and ultimately find a baptismal/birth record. Below is what comes up on the Madeira site:
If I'm reading that correctly, Francisco is originally from Faial, so I'd like to see if there is ultimately any link to Sao Miguel or if any of his relatives moved there. I don't know if these are the individuals I'm looking for since the baptismal record indicates a different last name than Maria's parents listed on the passport record. Interestingly, Manuel (the son of Francisco and Maria) married a Vasconcelos so maybe the family ties are there.
So where I'm at is I'm trying to figure out a.) Are there Hawaiian resources not found on Ancestry or Family Search (specifically the birth or census) and b.) where can I find the Madeira passport records so I can get Francisco and Maria's ages and hopefully trace them back to their origins?
Thanks in advance. Hopefully this message isn't too "all over the place" but if you have any questions, please let me know!