nephew
Great Uncle.
No relation
None. There is no relation through "my friend"
Yes.
They have the same mother and different fathers.
Real sister, half sister, or step sister
Your fathers brothers are your uncles. You are their nephew, or niece.
Your half-brother's full brother would also be your half-brother.Your half-brother's half-brother (assuming he isn't your full brother) is probably what we officially call "no relation," though he might potentially be a stepbrother.
Sid is Tom Sawyer's half brother because they share one parent in common - their mother. They have different fathers, which makes them half siblings.
it makes sense
Your half-brother's daughter is your niece. Your niece and your son are first cousins to each other.
Nothing really. There is no blood relationship between the two.