uncle
Besides immediate family, these things are usually settled on a case by case basis.
Your first cousin is the child of your parent's sibling. Your second cousin is the grandchild of your grandparent's sibling. So your first cousin is more closely related to you than your second cousin and is "first in line" if you leave no living children, grandchildren, parents or siblings.
Your mother's Father's sisters, no matter how many there are, would still just be his sister. Her mother is also his mother, your great grandmother, and her son would be your grandfather or your great uncle.
A child.
It depends on how the will was written.
Yes you are but not by blood. Distant related by marriage and can say cousin in law as you both connect into one family as both Aunt and Uncle but however not on same blood line.
A first cousin is the child of your parent's sibling while a nephew is the child of your sibling. That makes the nephew more closely related to you than the first cousin, unless the law in your place of residence defines things differently.
Yes, the baby would be your cousin one more time removed from your relation to the cousin. E.G - if your second cousin has a baby, the baby will be your second cousin once removed and if you have children, they will be third cousins of the baby.
No, your first cousin (whether twice removed or otherwise) is not in your direct line of descent and you can inherit nothing genetically from that person. You can inherit genes from your parents that your first cousin (whether twice removed or at some other removal) inherited from his parents.
Describing someone as a "distant cousin" is a very imprecise way of saying that they are related to you, but the speaker either does not know exactly how or they are not a first cousin, but are "more distant."
Your first cousin's sibling (parent of the nephew) is also your first cousin, so in that case the nephew is your first cousin, once removed.However, it's possible that the nephew is the son of one of your cousin's spouse's siblings, which makes him best described as "no relation."Then there's half-siblings, and step-siblings.... the bottom line is you're probably best off leaving it as "my cousin's nephew" except in the specific "cousin once removed" case already mentioned.
First would be spouse. If no spouse, then children If no spouse or children, then parents If no spouse, children or parents, then siblings. If no spouse, children, parents or siblings, then nieces and nephews. If none of the above, then the next relative in line. (Grandparent, aunt, uncle, cousin and so on.)