[ArathornJax]

According to Of the Rings of Power in the Silmarillion Gandalf and Saruman were the Istari on the Council along with "Elrond, Cirdan and Galaderial along with other Lords of the Eldar."

I think based on that we know for sure who was on it as has been posted. I would also agree that Galdor and Erestor were there as they were on the Council at Rivendell. Other than that I would say it is pure speculation.

In terms of the attack on Dol Guldur, I am believe this assault was on Sauron by the members of the Council, and not a physical attack with an army on the fortress. From below we know that the purpose was to force Sauron out of Dol Guldur and they did that. However the fortress remained (see below for more of this).

I looked at the Peoples of Middle Earth from HOME and did not see any reference to the attack. Again, the source I have found is in The Silmarillion in the same chapter Of the Rings of Power. There it says that Curunir (Saruman) wanting to prohibit Sauron from having free access to searching Gladden Fields and the River Anduin which were next to Dol Guldur consented to the attack. It says:

"Therefore for the last time, he aided the Council, and they put forth their strength; and they assaulted Dol Guldur, and drove Sauron from his hold,"

I wonder how Saruman aided the Council? However the verse "put forth their strength" to me sounds like they used their personal strength to attack, not an army.

As I further reflected on this, and that the text also mentions that Sauron had perceived what the Council was going to do and so this was really a "feint" allowing Sauron to return to Mordor (the nine Ringwraiths had already left to prepare for their Master's return), and whether the Council had used their personal strength to assault Dol Guldur, or led a force that attacked met I had to look further. So I did and I feel good that this was an attack of personal strength against Sauron because Dol Guldur was not thrown down in 2941, and remained standing until Celeborn took it after Sauron's defeat and Galadrial came forth and threw down its walls according to Unfinished Tales and Appendix A. If the Council had actually physically assaulted Dol Guldur in 2941 with themselves and an army, I would have imagined they would have done this at this point to prevent Sauron from having a stronghold to the north of Mordor), Sauron allowed them to "win" since it met his purposes. The next year the fortress was again occupied by a Ringwraith and evil returned to Mirkwood.

I could accept the Council physically attacking the fortress with an army, if we can find evidence on why they did not destroy it at that time, or even speculation based on something in the writings.

So, where am I on the questions?

1. Did the Wise really, personally, come to Dol Guldur? I don't believe so. I think they attacked from somewhere near, which would probably point to Lorien. It took a final victory by Celeborn after Sauron was defeated for Galadrial to come forth and throw down the walls, lifting the shadow from the forest of Mirkwood, which was then renamed Greenwood the Great. This may also be what Galadrial refers to when she tells Frodo that Sauron suspects that she has one of the three Elven rings but is not sure. If the attack was made from Lorien, this may explain one reason Sauron is suspcious of her.
2. Who was actually in the White Council? We know according to the Silmarillion that Elrond, Cirdan, Galadrial, Saruman and Gandalf were, along with other Lords of the Eldar. Anything beyond this is speculation at this point.
3. Were they all there in Dol Guldur, or someone stayed home? I believe they all were there except perhaps for Cirdan. He seems to like the oceanside a lot and I thought I read somewhere that he would not leave the Havens. That is speculation and would require me to do some research again.
4. Were they all alone in the forest, or did they bring an armed force with them?
See above. I believe they were alone in their attack per the fact the fortress remained standing.
5. If they did, whom did they bring? An Elvish commando from Lórien, or something else? Well, no one. If they did bring someone, I'm sure Haldir led an Elven force from Lorien with perhaps the sons of Elrond being involved. Might make a good piece of fan fiction.
6. Was there actually any battle? Did Sauron flee before the attack, or during it?
I think as the attack started Sauron departed. Once he departed, the evil things like Orcs fled since there was no leadership (and this seems to be a natural reaction for Orcs when their leaders depart or retreat.
7. How the battle looked like? Galadriel sings a song and half the wall of Dol Guldur's fortress crumbles down? Saruman shouts exorcisms and the spirit of Sauron flees? Or Glamdring swings above the heads of Orcs?
Saruman used some of his "devices" but we do not know what they were. I don't think they were anything to blow up the fortress or it would have been eliminated per above. I think these devices were something he discovered in his studying of the rings, and he revealed it so he could get what he wanted, Sauron out of the Anduin and Gladden Fields areas.

Just some thoughts.