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. Aerobic exercise does not build muscle tissue.