The question is that when applying for British Citizenship, do we need to fill in three separate forms? I mean while my child is entitled to apply by him/herself what are the implications of being included in one of his/her parent’s forms?
Whilst the Home Office will consider a joint application you must still submit two application forms in respect of you and your wife. Your child can be included as a minor in either one of the two forms and will be 'regsitered' as a British citizen whilst you an your wife will be 'naturalised' as British Citizens. Both status are the same its just the former is for under 18's. The advantage of a joint application is that you pay a single processing fee and are likley to get all stages of your processing done together right up to the citizenship ceremony. This assumes your wife and you both meet the residence requirements - if one of you doesn't then they have to wait for the other one to naturalise then apply separately as the spouse of a British Citizen for which the residence requirement is shorter.
It’s nothing wrong in including him/she in one of ours forms but then why was she given an ILR letter in the first place?
I assume you submitted his/her individual passport for ILR stamping which would be accompanied by a grant of ILR letter. In any case the Home Office will issue a status letter to each applicant for a variation of leave (change of status) including dependents.