Yes, you can. In the Related Link below, on page 16, under "What could disqualify me from receiving benefits", "What happens if I quit my job", item #3 says you can quit to follow your spouse due to their employment, etc.
Yes you can file
Yes, they do.
probably not
Yes, in states where same-sex marriage is legal, any employer which provides benefits to the spouses of its employees must do so regardless of their gender. To exclude same-sex spouses would be illegal discrimination, as those states all have discrimination laws on the books.
Yes, it offers all the same benefits it does to opposite-sex spouses.
ex-spouse that has a special needs child, are they able to receive benefits
By law, all US companies offer benefits to same-sex spouse IF they offer benefits to opposite-sex spouses.
Yes, it offers the same benefits to domestic partners (both same-sex and opposite sex) as it does to spouses.
Yes, Yahoo offers the same benefits to domestic partners (both same-sex and opposite sex) as it does to spouses.
10 yrs What if they have been astranged for that long
10 years
In the tables in the Related Link below, (effective 01/03/2010) it gives your weekly benefits for those who earned, in their highest 2 quarters from $800 to $21,255+, for individual claimants, those with spouses and those with child. The second Link below gives the formulation on how it arrived at.