Nick,
Congrats on the new house then. A house
like that is lots of $$$ around here.
I hadn't seen the palm in your pictures and
assumed that was it. Sorry about that.
Your palm looks like a Phoenix (date palm),
I can't tell which, most likely Pheonix canariensis
(Canary Island date palm), Phoenix dactylifera (Date Palm)
or maybe Phoenix rupicola (wild date palm, india palm),
I don't know what grows down there.
Around here we have the canariensis and they are awesome.
AFAIK all Phoenix grow slowly and the first leaflets
on the petiole develop into spines.
I would clean it up by removing the dead and loose stuff.
I think they look best with a full head of fronds, a bit
like Sideshow Bob.
Btw, If you have an Oriental cherry, you will get
pretty flowers but most likely, no fruits.