It is absolutely normal for the pygmy date palms lower fronds to yellow then die. Whether or not this is what you are experiencing is hard to say without a photo. If it is the lowermost fronds I would not worry.
And there is no reason to water any palm or cycad daily. I would do two or three times a week at most- sounds to me like you are overwatering.
The fact that things flourished when neglected tells you something.

Your local cooperative extension office is a world of help. They are in the white pages under county and they live for questions like yours. If you stop by the office they will have tons of printed info to give you and will answer any questions you have.

I do think overwatering could be a problem. Its hard to overwater plants when its warm outside, but when its cool (60s and 70s) then many palms really dont require too much water (there are many exceptions, but Pygmy palms arent one of them!). Cut off all the dead fronds and if the lower fronds are yellow, cut those off as well. If all the fronds are yellow, that is a problem (likely an overwatering problem). I could be a nutrient problem that more magnesium and/or nitrogen should take care of.
Sago palms are actually cycads (but thats fine here since this is a Palms and Cycads fourm!). They are one of the easiest plants you can care for. Basically do nothing and your good. If its very warm and dry outside, some water will be really good for it!
Queen palms is one of the most beautiful palms you can own if its well taken care of, but easily one of the ugliest palms in the world without proper care. They will survive pretty much anything, but as far as looking good, they need a good amount of fertilizing during the warm weather months, and they definitely need a good amount of water on warm and sunny days. Prune off the dead fronds and after that, it should do very well!
-Alex