It sounds like she is injecting heroin. The spoon would be used to mix and heat the drug. You may find needles around your home so you would need to be very careful when reaching your hand into anyplace you can't see. Some addicts do share needles even though it is a high risk action and you do not want to get stuck with dirty needle.
My husband is a heroin addict (IV) currently in recovery. The nodding out sounds like him. I don't know if it matters if she falls backwards or forwards, or even what drug she is using. The fact you and your husband will have to deal with is what you will and will not accept from her while she is living in your home.
Is she wearing long sleeved shirts? That can be another sign of an IV user...covering up track marks.
So sorry you are dealing with this. Glad you joined us.