Yes, the headphones logo is still there after the ear phone is plugged out of the phone. There is incoming call but when you pick up the call, I cannot hear the other party at all. I then turn on the speaker and only then I can hear the opposite party
For the headphone problem, some users have gave feedbacks that if you repeatedly plug in and plug out the earphone, the logo will disappear. This is sometimes due to the headphones itself, as well as phone's sensors not being sensitive.
I once had a phone where its audio jack spoilt any earphone that was plugged into it.