Mature robellini Palm questions

This palm was in my front colorful island when we bought the house, and we love it. I have a few care questions.
See pic #1. In the top, under the canopy, there seems to be a lot of brown dead-looking stuff. Am I supposed to let that fall on its own, or clip it off now?
See pic #2. In the top, there are a lot of Bright green strands that have little "balls" on the end. Should I trim these off before they make seed? Or are these new fronds about to make?
Thanks so much for your help,
Jojogarden

In pic #1 those are the old dead flowers and you can clip those off any time. Pic #2 is the developing fruit. You may also cut those off at any time without harming the plant at all.

Thank you very much, QCHammy