Are people with HIV susceptible to sepsis?

May be. Pneumcoccal sepsis/pneumonia and salmonella bacteremia were two illnesses seen in HIV infected people especially in the pre-therapy era.
Very much so! Because their immune systems don't work normally, people with HIV are more likely to develop sepsis from an infection.
Yes. If the infection is not under control. If HIV is well treated and viral load undetectable, cd4 count normal, then the risk is less.