Is it bad to use MacBook pro with battery every day. Is it bad to use new MacBook Pro with battery every day? Or would it be better for the battery lifetime to use battery only one day a week? 

The problem is that I don't think I can change battery if it gets bad...it's built into the MacBook I think.
There is no harm in running on battery most of the time.

To get the most out of your MacBook Pro's battery, follow the Notebook Battery advice from Apple: unplug and use your battery until empty about once a month, then charge back up to full.

If you need help following Apple's advice, use Battery Guardian; it is free and will remind you when to deplete your battery.