Can my twin brother sponsor me and how long is it going to take?

It is currently taking about 12 years for a sibling of a US citizen to qualify for a visa.

Yes he can petition you. However, currently and depending on what country you are a citizen of, there is at least a 12 to 24 year waiting period before a visa is available. I suggest to consult with an experienced immigration attorney about your situation.

That depends on a lot of things, including but not limited to your country of origin and whether you have a currently valid immigration status. You may want to consult an Immigration Attorney in order to find an answer to your question.

You are not forbidden to apply for the residency in the US via asylum and through the petition of your brother. However, the latter might take a long time to process. Nevertheless, the earlier you start, the sooner you will get in-line. If your asylum application is approved, you pass your asylum interview, you will be able to cancel your brother's petition. If you will not pass the asylum interview and are referred for the removal proceedings in the immigration court, it might take from 1 to 3 years to resolve (one way or another) the issue with immigration judge. More depends on your asylum application. You would be better off to discuss your particular situation with an immigration attorney.