False. Say you're eating 3000 calories a day and you exercise for an hour per day and burn 500 calories, but your caloric maintenance is 2300 calories. So you're at 2500 calories but you need to eat less than 2300 to lose weight. [1]
If you do not know how many calories you are eating, and your maintenance level you will not be able to ascertain the correct level to lose weight. You can exercise all you want, but if you're eating more than you're burning you will not lose weight.
[1] https://en.wikipedia.org/wiki/Third_law_of_thermodynamics and it in practice http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2763382/
>A bit of regular exercise will work for all but the most silly examples.
I do not think it's wise to make such a large and unsubstantiated blanket statement, as I have mentioned prior it comes down to how much you are consuming and burning each day, over a prolonged period of time. It is also not helpful to say 'a bit of regular', that statement is hazy and it's impossible to know what you actually mean.
Nop, you can still eat enough calories to gain weight while running a marathon every day.
Eating at a caloric deficit isn't independent of eating micronutrient dense food.