Of course. There is no reason unless there is a cleft palate or anatomic defect or have been recommended to avoid having the baby drink from a cup. Is there any reason the baby can't drink from a cup other than it is too immature at the current age?
Yes. You can have your baby practice drinking from a cup at any age. Be ready to get a little messy in the process.
6 months. Once your baby is able to sit up in a chair to feed, let him/her practice drinking with a cup.
It varies but... When your child starts to make the switch from formula to starter food you can start to introduce a cup for liquids. Remember not to stay with a "sippy cup" for too long as your child can develop an open bite in the front teeth. Best to try to move on to a regular cup when they are up to holding it.
Go ahead and try. With the plethora of baby supplies available, from special bottles to sippy cups with a variety of valves, a baby can drink from a cup almost as soon as s/he can hold one. Babies will usually show interest in cups/table food and you may use this as your cue.