None of the things you’ve mentioned would in and of itself prevent you from adopting but I would echo what @Ted27 has said.
You need to be in a stable place in your physical and mental health and in a good place financially. For example, if your health has prevented you from working, I’d wonder how you’d have the physical and mental resilience needed to parent an adopted child. I’m not saying it’s impossible, I’m saying you would need to build enough resilience to be able to cope.
Social workers need to know you’re likely to be able to care for a child to adulthood and support into adulthood. That includes things like expected life span, as well as not having foreseeable health issues that might render you unable to put your child’s needs first. If you look at some of the threads from parents with newly placed children you’ll get a sense of the demands that will be made of you and the challenges you’ll face. None of those experiences are atypical and you need to be able to be steady enough to cope.
The other part is your mental health, in terms of the violent behaviour as a teenager, you will need to be able to talk about this openly. That mans reflecting on what was happening for you at that time, what prompted the violence (and what the violent behaviour actually was), and the work you’ve done to overcome this. Being able to understand yourself at that time in your life is absolutely crucial because children will trigger you in all kinds of ways and social workers need to know that you have ways of coping that don’t involve violence.
In terms of being cancer free, a lot will depend on the type of cancer, the recovery rate, how you respond to treatment and the ongoing prognosis. I’d expect them to ask for an early medical and those findings will be an important part of the assessment. I’d also expect social workers to explore with you the impact of your physical health on your mental health and well-being.
In all honesty, you need to focus on your health and recovery first, and then focus on being able to get a job and sustain yourself in the workplace to provide a secure base to work from. That may take a few years in any event so try not to worry about 5 years cancer free, because you’ll need that time anyway.
You’ve had a lot to deal with over a protracted period of time and it sounds like the idea of not having children has been a huge blow for you. Give yourself time so that when the timing is right, you go into the process in the best place possible.