Young Children (say, about 5 years old) do not have the obligation and are not supposed to join Salat; they are not fully able to understand the meaning and to do everything properly but they like to be part and imitate what they see.
Is it allowed/well-received to let them participate in the way they are doing it?
If not, should they participate under age when they want and learned to do everything properly (e.g. 8 years old)
Answers according to any fiqh are welcome, Hanafi preferred.
Before puberty there is a stage called Tamiz تمییز which is when the child gains some understanding of things. At this age, acts of worship such as Salah are valid, although not obligatory. There are ahadith about performing salah at this stage such as:
مروا أولادكم بالصلاة وهم أبناء سبع سنين
Command your children to pray when they become seven years old
فقدموني بين أيديهم، وأنا ابن ست أو سبع، سنين
Amr bin Salama said: ... They therefore made me their Imam (to lead the prayer) and at that time I was a boy of six or seven years
— Bukhari
If the child does not yet understand things, or makes mistakes and can not pray properly, then you can still let them imitate you since this is a form of learning and motivation and will be beneficial.
