"This is my mother."
I think it is also fine to leave out the 的 when talking about one's own family members. 我妈妈，我弟弟，我哥哥, etc should all be fine to say as what I've learn from my classes.
I'm a bit confused, the explanation said whenever I use "this" or "that" I should add the measure word "gè", any help? Also maybe it's my bad ears but I hear the tone as "ge"
個 is a generic noun classifier. With people you wouldn't use it. It takes some practice to see the correct usage in many different contexts.