Have Avaya phones when people call in it disconnects them after message finish

On most phones, a red light indicates a message in voicemail. You need to press the MESSAGE button and follow the instructions on pages 4 and 5 of this reference manual.
https://downloads.avaya.com/css/P8/documents/100130184

Try disconnecting from battery, if it is the security code wont be removed

There are two user manuals for this phone from hell.
The 102-page "Quick Guide" and the 410-page "Advanced".
Pick your poison, but you'll probably need the advanced. Just search on "attenant" and you'll find what you need.
Quick: https://downloads.avaya.com/elmodocs2/partneracs_r4/456804_2.pdf.
Advanced: https://support.avaya.com/elmodocs2/partneracs_r3/456803.pdf
May the phone be with you...

No, that will not disconnect the caller. BUT, if you hit the headset button again, it will.
If you hit the headset button, you need to hit the switch hook to regain the call....

What voicemail do you have?

Multiple login error will clear up if you reboot your phone system with voicemail.

Try to delete all the messages then try adding a voice mail dialing from another extension then you will recieve the messages.

Do you know which system this phone is on? Is it an IP Office?

If so, chek the manager program and verify that under eachs users tab, ther is a "Vxxx" in the "trusted source" tab. Where "XXX is the extension number.

If the voicemail you want to use is Verizons, it will NOT light the light on your phone.

For that to happen, you would need a voicemail through the phone system

What is the admin extension are you logging into?