call logs

do calls that i do not answer show up on my call log. 

will  people that call and leave a voicemail when my cell phone is on bedtime mode, show up on my call log? will i get the voicemail also?

if my cell phone is off and someone calls will that call show up on my call log?

i have someone trying to say that they called me but their number does not show up in/on my call log on my cell phone and also in/on the call log on t-mobile.com. i also do not have the supposed voicemail they left. is there anyway that t-mobile logs the voicemails?

my cell phone is a moto g stylus 5g, the cell phone would have been on during the time they called.