Could the time of day when you take your exercise have negative effects on your body?

Yes. Studies have shown that exercising within 2 hrs of your planned bedtime can not only interfere with sleep, but also set your body's melatonin secretion cycle out of wack. Therefore, earlier is better.
Yes. You shouldn't exercise before bedtime( at least 3 hrs before), could exacerbate gerd and produces insomnia.