Cramps have lots of different causes. You need to consider dehydration, salt deficiency, potassium or calcium deficiencies. You need to analyze your own situation. A heart rate monitor is good for reminding you to go easy on easy days, but you don't really need a monitor to tell you that. What cross training you do, again, depends on your own goals.
Cross training is a myth, because muscular activity is so sports specific.
Cross training can be helpful for overall balance. It does offer a good alternative in the off season or in bad weather. We get old because we're inactive. We don't become inactive because we become old. Muscles atrophy by lack of use.