I am a US citizen and want to apply for my brother, is it true that through my parents (green card holder) is faster?

Yes, it is true: if your brother is over 21 and not married, his permanent residents parents' petition can result in an immigrant visa for him in 3.5 to 4 years faster than your petition. Keep in mind, though, that, if your brother is married, you can petition for him but your parents can't - until they become U.S. citizens.

Yes, it is faster through your parents but still about 4-6 years, minimum. For you to apply for him, it will be about 10-12 years.

(brothers and sisters of adult citizens) category has a longer waiting time than F2B (unmarried sons and daughters (21 and over) of permanent residents) and F2A (spouse and children (below 21) of permanent residents) categories. If your brother is below 21, the waiting time is about 2 years for all countries of charge ability for F2A category. The waiting time for F4 is about 11 years for all countries of charge ability other than Mexico and the Philippines. For Mexico and the Philippines, the waiting times are 16 years and 23 years, respectively. So the waiting time difference ranges from 9-21 years, depending on your brother's country of changeability. If your brother is 21 or older and his country of changeability is other than Mexico and the Philippines, the difference is about 3 years based on the November visa bulletin. If your brother's country of changeability is Mexico, the difference is about 4 years. If it's the Philippines, it's about 13 years. In deciding who should file the petition, I think you should also factor in the age and health condition of your parents and the likelihood of your brother getting married before your parents could file for citizenship. The death of a petitioner before a visa is granted to the beneficiary results in the automatic revocation of the visa petition (unless 204(l) applies). Also, if your brother is petitioned by your parent and he gets married before the petitioning parent naturalizes, it will also result in the revocation of the petition because there is no visa category available for married sons and daughters of permanent residents.

No, if you are the US citizen, it will be faster processing if you file for your brother. For quicker processing by your parents, they would have to become US citizens, and then get priority processing.

Yes, but your brother must remain single unless the parent can later become a citizen.. And it is not true if your brother was born in Mexico.