Unfortunately, the US immigration laws do not allow grandparents, or extended family members such as cousins, aunts or uncles to qualify for greencard petitions unless they have a closer family member such as a US Citizen or lawful permanent resident parent, spouse , US citizen brother or Sister that can apply for them .
The answer is yes if you are at least 21 years old and a US citizen. US permanent residents are not eligible to apply for their siblings. Since siblings are deemed eligible for an immediate visa, they must wait after the USCIS approves their petitions for the priority date of their application to be reached by the National Visa Center until an interview will be scheduled for them in their home country. This could in many instances take several years.
The answer is yes. Whether you are male/male or female/female , the filing requirements are the same as with any fiancée visa, in that you have to have a US citizen petitioning for you, prove you met in person within two years, and establish your intent to marry within 90 days of entering the US. The process isn’t anymore difficult for a same sex couple as a heterosexual couple applying for a K-1 visa.
There are a number of different ways for a person to become a permanent resident. These qualified applicants can be immediate relatives of US citizens, such as spouses, children, and parents. Preference relatives of US citizens and Lawful Permanent residents. Employees and Workers at US companies. Investors with substancial assets. Also being selected from the Diversity visa lottery, that awards 50,000 green cards a year. Special Immigrants, such as religious workers. And finally, those who have qualified for cancellation of removal in immigration court.