What are you worried about in the kitchen? If you have reason to suspect that the person brings non-kosher into their kitchen or doesn’t keep milk and meat separate then by all means, don’t trust them (I certainly wouldn’t!). But without reason to suspect anything, ?? ??? ???? ????????.
Regarding cholov yisrael and cholov stam: If you believe that cholov stam is actually ??? ?????, then you probably shouldn’t eat food that was made in pots that were used to cook with cholov stam. (I can think of reasons to be lenient even there like ?”? ?? ?”? and ???? ?? ????, but I’ll leave that aside) If you believe that cholov stam is ????? ???? ???, but you want to be like Rav Moshe’s ??? ??? ?????, then you should be okay eating from those pots.
To clarify what I mean when I say ?? ??? ???? ???????? – you can trust somebody that his food meets the standard that he purports to keep. For example, you can trust that the meat in my house is glatt kosher (unless you don’t trust me, which is fine being that I am anonymous), but don’t assume that my challah is yoshon unless I knew you were coming and checked to make sure the flour was yoshon before I served it.