There are various conditions attached to entitlement to Child Benefit. One of these is that the claimant has to be ordinarily resident in the UK and not subject to immigration control -broadly this means they must have no restrictions entered in their passports & no condition that restricts their right to claim public funds. Generally speaking, if they have lived here for 5 years, are working and have NI numbers then they should have no problem. I would suggest they submit a claim and see what happens unless they do have a condition that says they have no recourse to public funds.
I am not aware that Child Benefit has to be in payment in order to claim DLA for a child. Again, submit a claim & see what happens. If there is a query, say that the CB claim has been submitted.
If for any reason they do not have NI numbers the whole thing is more complex, as these are needed in order to claim the benefits.
As well as CB & DLA they could claim tax credits if their income is low enough.