Is a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?

A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.

There is a job opportunity in the Nuns Hospital. Is it allowed for me to take this job given the difficult living conditions and the high rate of unemployment?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

If your work is lawful and has no effect on your beliefs, then there is no sin on you and do your best to represent the true face of Islam. And Allah The Almighty Knows Best.

Is it permissible for us to sever ties of kinship if our blood-relatives` gatherings/meetings involve acts of sin?

Observing kinship ties is obligatory, and paying your blood-relatives a visit causing their sinful acts to be hindered , then you should do so. However, if their sinful acts continue while you are at their gathering and they didn't respond positively, then observing kinship ties via telephone and the like will suffice in this case. And Allah Knows 

Is it permissible to offer the Eid sacrifice in a non-Muslim country?

Eid sacrifice is permissible anywhere, and Islamic Sharia hasn`t determined that it should be in an Islamic country, but poor Muslims should be given a share in order for it to be valid since it is an act of worship. A portion of that Eid sacrifice should be given at least to one poor Muslim, and if that wasn`t possible then the one offering it should consume it along with his family.