From my experience of palms, I would, with no hesitation get rid of them. Apart from the viscious thorns and poisonous fruit, if Costafinca's ID are correct, they just LOVE underground storm water and sewage pipes. The ponytail (Beaucarnea or Nolina recurvata) is not related to the palms in any way and is a plant I had growing in the garden of my place in Queensland (before the local Power station bought it out from under me, but that's another story. :-) ) Its roots are fibrous and non-invasive. Masses of small white flowers and one I would gladly have again, if I had the room in my current garden.

Hi would suspect you have something digging up the roots?? Queens usually root very easily, 6 months tops Are you in florida?? maybe too much water?? gary

Coconut palms, especially Jamaican Talls, are known to have a lean to them.

They are a slow growing palm. Strong direct sun and plenty of water are the main requirements. They're often grown in ponds. You'll always get a lot of suckers around the base of the plant. People tend to trim those off so the older colourful trunks remain visible. You can do it any time. It doesn't affect the plant.