Is it forbidden to go out with a Russian girl in public places and parks if the intention is to introduce her to Islam?

You are not permitted to go out with this girl, as it is the essence of temptation, given her immodest display and lack of shame. Furthermore, merely going out with her involves cooperation in sin and aggression. Your conversation with her is forbidden except out of necessity or need, while adhering to Sharia guidelines. As for inviting her to Islam, this can be done through believing sisters, because your effort to guide her should not lead you astray.