A child can go to the bathroom alone at night by the ages of 3 to 4 years old.
If the child can go pee without assistance and they know where the bathroom is then they should be able to get up, go to the toilet, pee in the toilet and go back to bed.
A child certainly by age 4 to 5 years old should be able to go to the bathroom alone at night.
In public though even a 5 year old should be accompanied into a public restroom for safety reasons even if you have to take them as a boy into the girls restroom.
I would not allow a child in these days and times to go alone to a public bathroom until at least 8 years old.
A 3 year old can usually wipe themselves somewhat but they may still require some assistance until around age 4 years old to ensure they get their bottoms clean enough.
It's still good to have the 3 year old help wipe themselves so they will learn but you still may need to assist them.
As your child reaches the age of 3-4 years old, they should be able to wipe their own bottom after a bowel movement.
Essentially, by this age and older, most kids should be able to wipe their own bottoms without much help from an adult and drawing closer to being done with potty training.
A kid is not potty trained if you have to run them to the toilet and remind them all the time.
In those cases it's really the parents that are potty trained.
A child is potty trained when they can go to the toilet on their own, wipe their butt and pull up their pants, clothes etc.
Some kids don't get potty training until after 3 years old whether a girl or boy.
In reality there's no best age but the best age to potty train your toddler whether a girl or boy is when they are ready.