1) What is the estimate of h^2?
Technically, HIV is not genetically heritable since there is no 'HIV gene' that codes for the disease. Likewise, HIV is predominantly transmitted via non-heritable pathways: unprotected sexual relations, unscreened blood transfusions, needle-sharing, etc. However, there a certain instances when HIV is heritable from mother to child. The transmission of the virus from the mother to the child can occur in utero during pregnancy and intrapartum at childbirth via the placenta. In the absence of treatment, the transmission rate between the mother and child is around 25 percent (Coovadia). However, where combination antiretroviral drug treatment and Cesarian section are available, this risk can be reduced to as low as one percent (Coovadia). Breast feeding also presents a risk of infection for the baby.

Coovadia H (2004). "Antiretroviral agents—how best to protect infants from HIV and save their mothers from AIDS". N. Engl. J. Med. 351 (3): 289–292.

2) How much influence does selection have on this trait?
Selection starts to influence the transmission of HIV when the person develops AIDS and begins to get sick. While the person is infected with HIV but not showing symptoms of AIDS, selection does not influence it. Concerning the virus itself, selection plays a big part when it is being medically treated. Selection influences HIV as the virus rapidly mutates at random and creates new strains of the virus within the host. Through finding treatments for the virus, the strains which are resistant to the treatment are selected for and become prominent within the host. If the treatment changes or is terminated, a new strain may be selected for. For example, when AZT is being used to treat HIV, the viruses with the mutation to recognize and circumvent AZT will survive while those without the mutation will not.

3) What effect would inbreeding have on this trait?
Inbreeding does not effect the transmission or development of HIV.