The software is very easy to navigate. It does only work with the nvr it is not known to directly work with other manufactures cameras. As long as the NVR pulls the video from the cameras you will be good.
The cameras should work, please keep in mind you will want to have the cameras updated before you begin adding them to the new NVR. The NVR supports axis protocol and ONVIF, but back to firmware any changes or issues that may have been found would be fixed with a firmware.
As you want to mix equipment I am not sure that all the features of your IP cameras will carry over. You may have to login directly to camera to make the needed changes. The camera with the joystick is hard to say what will or will not work. The spec sheet on the camera does not detail the version of ONVIF it uses. Typically we can move a PTZ camera with the NVR and not use a joystick. Depending on how the joystick talks to the camera would depend if you can still use it or not after connecting it to the nvr.
The fish-eye cameras in theory would work with the nvr. Our NVR breaks up our elite fish-eye camera into 12 views if you want but it only records the main fish-eye view. If the nvr can handle your fish-eye the same way then the software would display it as such.
On the DVR you have with the one analog camera you maybe able to port that feed over to nvr from dvr. Just like the dvr is a IP camera. I could not find anything to support that idea though, so I do not know if it would work.