Do you need a mechitza for cousins? If we are at a grandmothers house can we sit at the shabbat table mixed males and females 1st cousins? 2nd cousins? is there a difference if we are eating, talking or playing driedel on chanukah?
Also is there a problem giving them a hug? If yes is there an age limit, say its OK to hug a 3 year old but not a 10 year old cousin? Where can I learn more about this?
There are no “hard-and-fast” rules about family members of varying degrees sitting together at meals. For older children (9+), who become sensitive to gender issues, cousins should not be seated together, but it is mostly sufficient to seat at two sides of the table, and there is no obligation of a mechitzah.
Concerning hugging, it is okay to give a hug to a young cousin (3-5), but not to an older cousin for whom the issue of hirhurim are relevant. As the Chazon Ish writes, it is difficult to set a precise age for this.
See Iggros Moshe, vol. 2, Yoreh De’ah 137 (concerning sisters); Chochmas Adam 135:1 (concerning relatives), and 134. See, at length, Nit’ei Gavriel, Laws of Yichud, pp. 339ff, who quotes many details of these laws.