I identify with the tea party movement, or at least the initial founding concepts of the movement. I'll answer each question you raised in some detail, since my position can be a bit more nuanced than just FOR or AGAINST.
Gay marriage - I'm opposed to government trying to redefine a cultural and religious institution that has a very long tradition as being defined as being between a man and woman. However, I'm not opposed to Civil Unions that grant the same legal rights and protections. I don't think there is a "right" to it, but I don't oppose it.
Spousal Rights - I guess my feelings would've been covered under my answer for gay marriage.
Adoption - Gays should absolutely be allowed to adopt. The traditionalist in me feels that the optimal situation is a household with a man and a woman, but there are so many children who need adoption we shouldn't limit our selves to only the most optimal settings. If a person or couple is financially secure and emotionally stable, they should be allowed to adopt. Who they get their rocks off with really doesn't matter.
DADT - I think eventually it should be repealed. Other nations allow gays to serve openly and they seem to manage just fine. But I don't think now is the right time, with our troops serving in combat. It will unquestionably have a negative short term impact on enlistment, re-enlistment, and unit cohesion/morale. Once the troops are home safe and sound, then we can deal with the issue and iron out any wrinkles that come up.
Anti-Discrimination - I'm all for laws prohibitting the government from engaging in discrimination. I oppose laws that apply that to private businesses and my opposition is not limited to gays, I feel that way regarding race and gender as well. Anti-discrimination laws may have once been needed in the name of the greater good, but open discrimination of people is no longer acceptable in most communities. Therefor, I feel we need to return to protecting our constititional right of freedom of assembly (which includes deciding who we will assemble with). Plus it has the advantage of bringing the real backwards bigots out into the open so they can be treated with the disdain they so richly deserve.