1. You cannot have an approved homestudy for any kind of adoption if you are on public assistance, and must wait until you are off it and have steady income from another source for a period of time. You will have to check with a homestudy agency in your state to see if disability payments are considered public assistance. Many people with disabilities have adopted -- I've met adoptive parents who use wheelchairs, as well as those who are blind, but I suspect that most are employed.
2. In general, if you are expected to have a normal lifespan, and are physically, mentally, emotionally, and financially able to meet the challenges of parenting an adopted child, you may be able to adopt domestically. (Be aware that, because of issues arising from a child's life experiences and/or a birthparent's health, an adopted child could present more challenges than one who is born to you.) You will probably need to provide medical documentation that your disability is unlikely to shorten your life expectancy or make it exceedingly difficult for you to meet a child's needs. A person who has had a life threatening illness, such as certain cancers, will have to submit documentation that he/she has been in remission long enough that the illness is unlikely to return. Now, if you want to adopt internationally, you may have greater difficulty getting approval. In most of the countries from which Americans adopt, people with disabilities do not have the opportunities that they would have in the U.S. In addition to not getting the best medical care, they may face discrimination in education, employment, and family/social life. As a result, the adoption officials may not fully understand how well many people with disabilities can function in the U.S. Some countries forbid adoption by people with certain conditions, including survivors of cancer, people with mental health disorders stabilized on medication, and so on.
3. Single women generally have little difficulty with domestic adoption, as long as they meet the same requirements as married people -- for example, having a safe and welcoming place to live, having a stable source of income, having no criminal history, having no history of drug or alcohol addiction, etc. However, in those adoptions where the birthmother plays a role in choosing the adoptive parent(s), some birthparents may not be willing to place their babies with single women. Single men may be able to adopt domestically, but should expect greater scrutiny, as some people have a bias that single men are more likely to be pedophiles, child traffickers, etc., and are not as nurturing as women. With regard to international adoption, few countries accept single men; some, but not all, accept single women.
I hope this helps. Frankly, I have seen some folks with disabilities who parent as well as people without disabilities. But it's something that has to be considered on a case by case basis. One thing that I'd encourage strongly, in many cases, is that a person with certain types of disability might want to adopt children with the same disabilities. If you've seen the "Little People" TV shows, you'll know that some people with dwarfism can be marvelous parents for children with dwarfism. And I've seen deaf people parent deaf children beautifully. And some people with HIV commit to parenting children born with HIV, because they know that many people would not want to adopt children with this medical issue.
Good luck to you.