Is it normal to take my step daughter to my house and watch movies?

Some months ago I decided to leave the house were I was living with my couple and her daughter. I decided to leave because we used to fight a lot and she was sometimes yelling me in front of her little girl, that by this time I consider my daughter too, since we were living as a family and she called me dad, we created a very affecive relationship, I have a daughter too but shes not with me so this is another cause to keep closer to my step daughter. She don't really treat her so well so whenever I met my gf and that little princess she saw a safe place on me. Shes 10 years but she thinks, acts and says as a 18 years old young woman. Since my gf and I are still keeping our love relationship, the only difference is that I have my place and she her's so she can do whatever in hers and me in mine and this formula is kind of working cause since this happened everything has become better and shes more in good mood and less aggressive.

She works a lot from morning to late night and I offered to take care of my step daughter so she was agree with it, so sometimes whenever I go out from work I go to see her at my gf's house and we watch movies and else and other times I take her with me at my place and we play video games or watch videos or movies. We really enjoy eachother company. However I'm not sure to be doing the proper since I'm seen alone with her taking her out from her house and taking her in to mine by people, neighbors, cameras, security guards, I just want to know if this could be bad seing or misunderstood by people; i really love her in a very nice sense and I like to take her out and then we come to my place cause after work Im so tired that I prefer to do it like that.

Is it normal to take my 10 yo step daughter to my house and have some sane fun? or maybe this can cause some kind of rumors or risk of what people can think or say? am I in risk by doing this with no bad intentions?