Simple door bell the light has gone out but pushing the door bell it stills work. The unit is wired. Do I need a new door bell?

THe doorbell is the part that's inside and makes the sound. You mean the outdoor button. Yes in most cases you need a new one. (the outdoor switch).. the bub in it has burned out. It will still work for years as-is. I know mine burned out years ago and I never got around to replacing it.

Yes, get a new one. They're only a couple bucks.

Disecting the doorbell switch and replacing he lamp with an chip LED and a resistor works, but you'll never have to do it again.