Not to be too blunt about it, but in most (i.e., 99%) of cases, one
cannot improve one's IQ by, say, 30 points from age 12 to 20. What your cousin means by a "lot" may be the 8-10 points I mentioned (which is half a standard deviation, so it's not like it's insignificant or anything), but I dunno. I
do know, however, that I've read several journal articles which say roughly the same thing, and both my cognitive psych professor and the head of the psych department at my university said as much themselves. But perhaps she's doing some cutting-edge research into what factors would improve IQ and she's gotten some great results...I wouldn't know. There
have been studies which examined some of the sorts of activities you've mentioned and their effect on IQ, and, yes, they have been shown to be beneficial-- but usually within the 8-10 point (maybe it was 8-12, now that I think about it) range. Also, performance on IQ tests
can be improved through practice (either explicit practice or simply by taking many IQ tests and familiarizing oneself with the format); one can view chess, or perhaps playing logic games such as analogies, as a sort of implicit practice in a sense (chess less so, as it seems to be improving global mathematical functioning rather than performance on a specific mathematical/spatial task). Who knows.