The first palm is Caryota mitis, commonly called Clumping Fishtail palm.

The others look like Ptychosperma, probably P, macarthurii. Both these palm are spread by birds which eat the seeds. Not unusual for them to turn up in isolated places.

Thank you tropicbreezent for confirming these are not the same palms.

I like the fishtail palms since they provide filtered sun very nicely over my fish pond.

I noticed this palm when the leaves turn brown, the fronds do not drop to the ground like other palms. They seem to stay up there (for months. If you look at the first image there are many "branches" that have turned brown for months. I wonder if they will eventually drop?

I also wonder if it's possible to separate a shoot from the parent clump to plant is elsewhere. Difficult to impossible surgery perhaps?

Haven't tried splitting off any Caryota but I think it would be difficult. Here there's seedlings coming up all the time and I'm forever pulling them out. When a trunk gets tall it starts to flower. After seeds develop the trunk dies off. There's always lots of new ones to take its place. I chop off the trunks before they flower. Old dead fronds stay a long time, they're not a "tidy" palm. One thing to watch is that the seeds are very toxic except for some birds. Don't know how they would be falling into a pond, whether they'd be toxic to fish. It would be worthwhile checking up on that.

Also get lots of Ptychosperma macarthurii seedlings coming up, I'm a bit more tolerant of those. They're a clumping palm but don't get as tall as the Caryota.