I shall answer the best of my abilities, and chronologically

Ghosts, I beg you, give me guidance! Whom of the three must we focus on killing?
Andres has destroyed the hope of humanity. The town must proceed without hope, and simply for survival. The cultists are killers. Gasmask is a killer. Nyxius will destroy everyone.

Does the Ghost Council accept my offer?

Does the Ghost Council have the means to contact me in private?
We shall discuss this today and I will have an answer for you later. As to contact, we are also unsure of our means to contact you directly.
Was it a mistake to lynch Sasaki?
No, Sasaki has not appeared on the ghost council. Read the write-ups and the rules again. He was Mafia, just not actually Gasmask.

Was Elijah Beskar? If not, who was he?
Read the write-up again. (Thermal Mercury) TM is a ghost.

Who is the next suspect for Gasmask? And is Gasmask male or female? O_o
Your guess is as good as ours on both counts.

What of Joooray, Khazaar? Are they still suspected? Should we lynch them?
Jooray is a possible suspect, along with Khazaar. As to lynch, both are good prospects.