Can a step parent get custody of a child if they were not legally adopted by the step parent.?

Yes. If the step parent can show proof of biological parent being on drugs, etc and not properly taking care of said child(ren). Document everything in regards to when the child is with biological parent and any letters of concern from schools etc. Have a separate calendar for documenting everything. If you must use a note book make sure it is only for this purpose. My brother is going through a similar situation except the mother is still alive and their 4 children and her oldest from a previous relationship all live with my brother.

You've definitely got a case for a custody battle, especially if you've been a) living with the child and his/her mother before she passed away, b) legally married to the mother, and c) can prove the drug habits and unfit state of the father.

Yes if father does not contest it, and surly a judge would take this into consideration. Because it is usually based on the well being of the child. Seek legal counceling. Good Luck.