It depends on the context. I would use average if you’re talking about a mean. The average student studies for six hours a week etc If you’re talking about the quality of the student, again average is good to use. He’s neither top or bottom of his Maths class but merely average. Common has another meaning in English. It can also mean his manners aren’t so good, or he’s not of good upbringing. So I’d not use it. He’s so common, always swearing. I’d not use ordinary. There are better words

If someone performs in a somewhat proficient way, they're not terrible but they are not at the top of the class regarding grades either, it's best to say they are an "average" student. This would not be impolite and would be perfectly understood.

There’s no real difference. It’s assumed a rough sleeper is sadly homeless.