hi,
I can answer the citrus part lol. You can use a granular type citrus around the trees 3 times per year. Just remember Valentine's Day, Memorial Day, and Labor Day and that is 3 x/yr. Some people will use a acid fertilizer (like MG miracid) in smaller doses more often, but I only do that with the container citrus. As far as watering, deep watering once or twice a week is best in these hot dry climates to encourage the roots to go deep. (I know what you mean about watering and LA! ha! I almost never watered anything planted in the ground when I lived there!)
I would think any good palm fertilizer would be okay for the palms. I only have a few diff types of fan palms and a cardboard palm, and thats what I use. I have at times fed mine a little fish emulsion and superthrive which they love.
Another thing about some palms is, some types are very succeptible to a 'yellowing disease' and can start showing lots of yellowing of the foilage and leads to gradual decline and eventually death of the palm. I am no expert on that but you could ask on the palm forum here at GW there are lots of experts there. Hope this helps a little.
~SJN