Merely breathing faster won't help. Each breath will just remove less CO2. What you need to do is produce CO2 faster, which means increasing your metabolic rate somehow. That generally means exercise.

That is a form of exercise, so in that sense yes. It isn't significant, even on the scale of a year, but it is something we can calculate.

For practical purposes no. When you breath faster your body just gets rid of less CO2 per breath. The amount of CO2 your body creates for a given exercise level can be considered a constant.