At 3 years old most children are potty trained or at least nearly potty trained.
Some children are potty trained as early as 18 months and are using the toilet and no longer in diapers at 18 months while some children may not be ready to use the toilet until 3 or even 4 years old.
There's no set age where a child has to be potty trained or should be potty trained as all children are different and will use the toilet at different ages.
If a 3 year old is not using the toilet it's not a big deal and you should just continue to try and get them to use the toilet.
By age 4 though the child really should be fully potty trained and using the toilet because they will need to be out of diapers when they go to Kindergarten unless they have a disability or have an incontinence problem that requires them to wear diapers.
My son didn't get out of diapers until he was nearly 4 years old and during that time he finally took the diaper off himself and started using the toilet.
I kept letting him know about using the toilet and eventually he decided it was time.
So most 3 year olds are potty trained but a lot of 3 year olds will still be wearing diapers and not be potty trained.
As for night time they may still wet the bed and need to wear pull ups or diapers at night to keep them and their bed dry.