Okay, I'm only in highschool, so I can't say much outside of schoolwork. I gotten straight A's in highschool and some college classes I've taken without a problem, and the key to success is effort. I'm sure putting effort into schoolwork must be difficult in the situation that you're in, but to get good grades you must...
1. Listen the entire class time and take notes on important stuff.
2. If you don't understand something ask questions, or talk to the teacher outside of class. Ask around online as well, that's a good resource, you'd be amazed how well some people can explain things that you feel like you just can't "get".
3. Do ALL the work you're assigned, do everything they tell you to do. They went to college to learn to teach, you just have to follow what they teach.
4. Study, you don't have to be studying 4 hours a day or anything, but when you're at home and you have some spare time, read over your notes a couple times, spend a little time just reflecting on what you learned, what you got, what you didn't get, and if you didn't "get" something, look it up on the computer, talk to the teacher after class, or ask the teacher a question in class when they're reviewing it. Before a test, be sure to put in a good half to full hour of studying each day for the 4 or so days leading to the test.
Effort is really key, this is a lot of work, listening, writing, reading, etc, but if you just put in effort, listen, do you what you're instructed to do, and seek help when you need it, you should be fine.
Good luck on sorting out the other problems, all I can say is I hope you find a job somewhere and that you're able to find a way to care for your grandmother as well as sort out school and a job.
All I can do is hope, I wish I could do more.