slaves

Assalaam Alaikum,  I have a question regarding Muslim men having intercourse with their female slaves (see Surah 70 -Al-Ma'aij 29-31).this topic has been previously addressed, but the issue of it contradicting what the Qur'an says about adultery and fornication werenot.  Furthermore, there is a hadith which states: "Whoever fornicates with a free woman or a slave, then the child is a child of zinaa, itneither inherits nor does the man inherit from it," (Saheeh Sunanat-Tirmithee #2113).  These two seem to contradict each other as well. I know Islam eventually eradicated slavery because people freed slaves to get rewards, etc. but did itactually make it HARAAM (over time of course)?  Also, if everybody is equal in Islam, then why are there stipulations on marrying a "slave" (i.e. if you cannot afford to marry a "free" woman, etc)? Can you please clarify theses issue in as much detail as possible? JazakAllah khair for your patience and informed response.