A lady asks her 3 yr old daughter:
How many colours are in/are there in this toy?
What should be used :are in/are there in?
Should 'there' be used ?
A lady asks her 3 yr old daughter:
How many colours are in/are there in this toy?
What should be used :are in/are there in?
Should 'there' be used ?
Either version is fine, although, as mentioned in a comment, it would be better to say
How many colours does this toy have?
Unless, for instance, it is a toy which contains, for instance, coloured blocks, or something like that.
You are correct that 'How many colours are in this flag' is more acceptable than 'How many colours are in this toy'. It is probably because toys can contain many substantive things (other toys, pieces, components), but colours (an abstract thing) are not logically or usually considered one of them. Flags are pieces of cloth, and can only 'contain' cloth and colour (dye).
As already noted, the idea of colors "in" toys perhaps doesn't fit well, so to answer the question of using "there" or not, let's say we are asking about the number of marbles in a bag.
How many marbles are in this bag?
vs.
How many marbles are there in this bag?
Either is perfectly acceptable. I would probably omit "there". On the other hand, if we change the question into a statement, I would almost certainly use "there":
There are five marbles in this bag.
vs.
Five marbles are in this bag.
While neither of the above statements explicitly says that there isn't something in the bag other than the five marbles, I would say the first alternative somewhat suggests that the bag contains five marbles and nothing else, as you seem to be describing everything that is there, in the bag.