GracetotheHumble, I'm going to answer these questions using the wordage that you have used. You might find more nuance if I were to write otherwise, but I don't want to avoid the question you've asked by changing the wordage to answer one I'm more comfortable with.
1. Which Methodist denominations do not allow homosexuality and consider it sinful?
The United Methodist denomination allows homosexuality among its members, but not the practice of it among its clergy, and considers the practice of it incompatible with the teaching of the Christian scriptures. We do not officially use the term "sin" with regard to it any differently than we do any other activity that is incompatible with Christian teaching.
Free Methodists and Wesleyan Churches tend to be more conservative on this issue than the UMC, but I don't know their official positions.
2. Are there any Methodist denominations that do not ordain women?
To my knowledge, all of the major Methodist denominations do ordain women. I'm always learning that there are smaller splinter groups that I have never heard of before. Perhaps among these that number in the couple of dozen congregations there may be one or more that does not. I don't know.
3. What is the Methodist teaching concerning eschatology?
The Christ will come again to raise the living and the dead, and when he does he will reconcile the world to himself in all things, and then rule it forever.
4. What can you tell me specifically about being a Methodist - please share your testimony.
That's really too long for just a part of a post. So, briefly, I was raised a Methodist, the son of a pastor. Until the age of 16 it was just something that I did without much thinking involved. Then, through the sharing of a lovefeast, I had my eyes awakened to the reality that Christ's death on the cross wasn't just an interesting bit of history, it was something that involved me. I became aware that I believed that if I had been the only person in the world that Christ had needed to die for to redeem me from my sins, that he would have done so. And in that moment I realized not just that he loved me, but that I also loved him and wanted to live my life for him. And that is what I have been doing ever since.
Methodism is about a disciplined, pragmatic approach to life in the service of God. We allow a lot of latitude for people who think differently than we do personally to also be part of us as long as they are going in the same direction that we are -- that is all honor Jesus as Lord, and living as servants of his here and not yet Kingdom.