Section 7 reports are usually carried out by a Cafcass officer, or an independent social worker. A S7 report provides the Court with information and advice as to what (if any) Orders should be made to promote the child's welfare.
S37 reports are carried out by a Social Worker, and the court is asking the local authority to consider whether it should be taking further steps to protect the child. You can't apply for a S37 direction, but you may suggest it to the Court if you think it relevant.
S 25 of the Children Act 1989 sets out the 'welfare' criteria which must be met before a Looked After Child may be placed in secure accommodation. This is applicable to "looked after" children only, so not relevant in your situation.