Is there a way to disable jumping?

Try setting the players jumpSpeed to 0.

Is there a way to remove the jump button on mobile?

// This script Execution Mode must be set to Local.
import * as hz from 'horizon/core';

class DisableControls extends hz.Component {
  static propsDefinition = {};

  // Automatically called when the world starts.
  start() {
    // Disables the onscreen buttons for the mobile player who is set to the owner of the object this script is attached to.
    PlayerControls.disableSystemControls();
  }
}

So if disable system controls, I can still add my own custom buttons? I want to have one button on the interface but not to jump.