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
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.
10 years