You are his great-great-aunt (or great-great-uncle) and he is your great-great-nephew.
* A much less-used US term for the relationship is great-grandnephew which follows the logic that your niece's grandson is your sibling's great-grandson, so would have the same generation-separation from both you and your sibling.
The grandson of your first cousin and your grandson are third cousins to eachother.
They are not related.
They are your nieces and nephews.
The son of your grandson is your great grandson. You are his great grandmother or great grandfather.
Some nieces of sisters are related to each other and some are not. Your niece is the daughter of your brother or sister (your siblings). If you have more than two siblings and at least two of them have daughters, those daughters are your nieces and they are first cousins to each other. You can also have a niece who is the daughter of a sibling of your spouse. If two sisters have nieces who are daughters of their spouse's siblings, those nieces are not related to each other (unless the spouses are related to each other, as when two brothers marry two sisters)
If your great uncle married into your family some of his nieces and nephews are your aunts or uncles (or your parent) and some are not related to you at all.
Your grandson and your nephew are first cousins, once removed.
You and your great uncle's grandson are second cousins.
Yes, you are related to your brother-in-law's grandson. Your brother-in-law's grandson would be your nephew once removed. This means that you are not directly related by blood, but you share a family connection through your brother-in-law's family.
If your great uncle is the brother of one of your grandparents, his wife is your great aunt but their nephews and nieces onher side are not related to you. Those nieces and nephews (and their children the great nieces and great nephews) have no ancestor who is also one of yourancestors.
Your son and grandson may be father and son, or they may be uncle and nephew.
Call the great nephew Joe and the great aunt Pamela. If Pamela is the sister of Joe's grandmother or grandfather, then Joe and Pamela are "blood relatives." However, Pamela could be the wife of a brother of one of Joe's grandmother's or grandfathers and still be Joe's great aunt. In that case, Pam and Joe are not "blood relatives."