Yes, for larger microplastics. "Microplastic" means plastic particles less than 5mm in length. A Brita water filter will filter out anything larger than about 2 microns, which encompasses a lot of, but not nearly all, microplastics.

If this is a major enough concern to be worth spending some cash on, you can get much better water filters than the Brita that will filter out surprisingly tiny particles and get the vast majority of microplastics.

Probably some, but since these systems are always built with plastic parts, they likely introduce new ones as well.