For multiple cursor movements you usually can solve the problem by adjusting the repeats setting for that device.
Log into your Harmony account and go to your devices.
Find the device that is giving you problems and click on "Troubleshoot"
Select XXX "responds to some commands either too many times or only occasionally" and click on Next
Select "0" and click on Save
Select "Yes" and click Next to update your remote.
Follow the directions to update the remote.
Test it out and see if you still have multiple movements, if the device doesn't respond go back through these steps and increase the repeats by 1 and try again.
Keep increasing until it starts responding correctly.
For your problem with the projector not turning off you need to go to your projector device and click on Settings
Select "Adjust power settings" and click on Next
Select "I want to turn off this device when it's not in use" and click on Next
Select "A button on the remote for On, and a different button for Off" and click on Next
Select "I don't have the original remote, but I know the command that is used:" and pick "PowerOn" from the drop down menu then click on Next
Select "My device needs more than one command to turn it on and off." and click on Next
Select "I don't have the original remote, but I know the commands that are used:" and make sure "PowerOff" is selected in both drop down menus, then click on Next.
Click on Done.
Update your remote.
If you still have the problem, or if your projector was already set up this way then you probably have another issue. You may be putting the remote down, or moving it around too fast so the projector isn't getting both of the PowerOff commands, or you may need to increase the inter-key delay for your projector so it will recognize them as two commands instead of one long button press.