Good day to you,
I believe we need to start in 2 Samuel 15 to get more details on this. Absalom decide to conspire to elevate himself into a ruling position. We can see Absalom slandering the king's ability to hear the people and give judgements (2 Samuel 15:1-6). and verse 6 specifically mentions he was winning the hearts of the people by basically being a politician and sweet talking the people. As you continue on in Chapter 15, Absalom is getting the people to claim him as king in Hebron. He was starting a rebellion.
Continue the story through Chapter 19, you see David using his good friend Hushai as a secret agent and gains Absalom's trust. Eventually leading to Joab killing Absalom even though David asked his men not to harm him. but thats a side point.
The "we anointed over us" in question is the people of Jerusalem responding to David's return to Jerusalem (I take this as gossip of the town). In summation Absalom only shortly had power due to his own self-appointed rebellious movement. He won the hearts of the people but was not appointed to be king from a prophet or from God for that matter, which was God's command to His people is that He would appoint the kings of Israel. So to answer your questions:
When was Absalom anointed king over Israel?-- He wasn't officially king but "anointed" by the people through conspiracy and political movement.
Who did anoint Absalom?--the people of Jerusalem
Was it same anointing as when Samuel anoints David (1 Samuel 16:12)- Different, see my answer to your first question- the king of Israel is to be appointed by God and God alone.
I welcome any other comments to sharpen our knowledge, if i have made an error please let me know! May God bless you all. Speak the truth saints.