In HIV infected children all live vaccines are contraindicated. However since BCG is given at birth and most of the time since we do not diagnose HIV at birth, we give BCG to these children.
Measles and MMR should not be given if the child's CD4 count is low. Once the CD4 count improves, both these vaccines can be given. Similarly also for chickenpox vaccine. OPV should be given in all children as part of the POLIO ERADICATION PROGRAMME. However if IPV is avaiable, it should be preferred over OPV.

A child who suffers from measles develops life long immunity. Hence such a child does not need measles vaccine. However measles is usually recognized by the clinical manifestations which are so typical. There are other exanthematous fevers of childhood, which mimic like measles. Patients may mistake them for measles. Hence rely only on a doctor's documentation & not on patient's history about past episode of measles. When in doubt it is better to give measles vaccine as no harm is done even if patient has suffered from measles in past.
Measles usually gives life long immunity. Diptheria immunity wanes as the age advances and hence bosster doses with dT vaccine is advised for diphtheria every 10 years after the primary vaccination.