I have many reasons to believe that someone installed a keylogger or spyware on my iPhone 6. I have done a lot of research and cannot find the answers that I am looking for. I want to know if it is installed on my iPhone 6 and if yes then how to end

To install a keylogger someone would need to have physical possession of your phone for at least an hour.

If this is a possibility you cannot detect it, but you CAN remove it. Follow these instructions to do a DFU restore of the phone, then set it up as New. Do not restore any backups you may have. Delete all of the apps in iTunes on your computer, then download them again to iTunes or to your iPhone before syncing the phone for the first time.

DFU mode:

• Install the latest version of iTunes on your computer if it isn't there already
• Reboot your computer
• Disable any antivirus and firewalls
• Launch iTunes
• Connect the device cable to a USB port on the computer (not to a USB hub), but DO NOT CONNECT TO THE DEVICE YET
• Press and hold the HOME and SLEEP buttons at the same time for exactly 10 seconds, until the screen turns black, then release the SLEEP button but continue holding the HOME button. If an Apple logo appears while holding both buttons you held for too long; start over.
• While still holding the HOME button connect the other end of the cable to the device
• You should see a message in iTunes saying a phone in Recovery mode has been detected (it may take up to a minute for the message to appear). When you see that message release the HOME button and the device should restore. When asked DO NOT restore a backup; set up as a new phone.