You haven't even seen the clothes, so why assume or be worried that they will be inappropriate? If they were, would your ex say something or intervene in any way, letting the girlfriend know he doesn't approve, or you won't approve? My husband was married before and has 2 sons from his first marriage. When they were younger (i.e. between 6 and 9) I used to get them clothes all the time - if I came across stuff that was cute, and on sale, sure. Especially when it seemed like every pair of pants and jeans they had ended up with holes in the knees, or it was stuff from their favorite sports teams, and their mom seemed to really appreciate it. You didn't mention the age of your daughter, but I am guessing as she gets older, she may not want other people picking out clothes for her - she'll want to pick out her own stuff. Once my stepsons hit their tween years, I didn't buy them clothes any longer. As the parent of a daughter, I can understand the worry about what they wear and now appropriate it is, and you don't want someone else being "the fun parent/stepparent" and letting the child get things that you don't approve of. But don't assume worse, or start worrying about the future - if it comes up, that is the time to have a conversation about it, with your ex and the girlfriend, if she is still around at that point. Who knows, she could totally be on the same page as you as far as what is appropriate and what isn't.
As far as your daughter calling the girlfriend's family members Aunt and Uncle and such, I can also understand having an issue with it, but I would have an issue from the standpoint that they are not married yet, and we don't seem to know where this relationship is going. Once my husband and I got married, my brother did become "Uncle J" to my stepsons - and at least some of that was out of respect for the fact that he is an adult and older than them. In our family, titles like Aunt and Uncle are not just for actual aunts and uncles - my older cousins are Aunt and Uncle to my daughter, as well as certain close family friends. It's more respectful than just going by first names only, but not so formal as Mr. and Mrs. I can see where for your daughter, it may get confusing, but at the same time, at this point, telling her that she may NOT call these people Aunt and Uncle after she's been allowed to do so may create even more confusion in her mind, and it may be better just to let this one go. My stepsons call their mom's live-in boyfriend their stepdad, even though they are not married and have no plans to get married, and while I don't like it, it's also none of my business and not worth arguing over.
The thing I would probably have the most issue with is your ex not keeping his daughter over for overnight visits. Is he and the girlfriend living together or is she staying with him every night? Is he concerned about sending your daughter the wrong message or is it more about the girlfriend would feel put out if he wanted her to not stay overnight if his daughter is there? He needs to think about what kind of message that sends to his daughter if he's not willing to have her overnight if the girlfriend is there - basically, that she's not important enough to have her there, and sometimes put her first over the girlfriend.
I think also you might have to learn to deal with the fact that your ex is romantically involved with someone else, the relationship may progress to marriage or it may not, he may get involved with another someone else down the road, and this is the kind of stuff that comes with the territory, when another adult enters the picture. If you feel you can discuss these things with your ex in a calm rational manner, with the both of you keeping your emotions in check, by all means, you should. It's understandable that you might start getting all "mama bearish" and territorial, but if you can talk things out with the ex and the girlfriend, it might help you see that really, it's all going to be okay.