D.B.
You have quite a few posts on this topic, and I think the majority of opinions will continue to be that you cannot change what he says, does and thinks. You can only change what YOU do. Yes, it would bother me too if he asked our daughter about my activities, but I can't control that and I would know full well not to engage him on that level.
You have a visitation agreement and schedule. Use it. On his visitation days/nights, he TAKES your daughter to his house for their special time. He does not spend any of it in your house. Period. He picks her up at the door. You either tell him you have people coming over or that you are going out (and then you go!), but this is his special time with her and it's not to take place in your home. You have her at the door when he shows up, with her stuff or her coat or whatever she needs. If necessary, you have your keys and pocketbook in your hand, and you get into your car and leave when they leave. Better yet, have her sitting in your car or waiting next to it, with you in the driver's seat. And off you go. If you just drive around the block, that's up to you. But you leave.
Do not tell your daughter what you are doing. Do not tell her you are going to Baltimore or to a ball game or to a Springsteen concert or to the grocery story or anything! She is 7. You must assume that she will a) tell her father and b) think she's SUPPOSED to tell him! Do not put her in the middle by giving her any info on your plans. You have a cell phone and can be reached in an emergency, but the deal with your ex should be that someone better be bleeding or on fire if he calls you. So although you don't feel the ned to hide things from your daughter - you DO have the need. It makes you the subject of conversation between her and her father, and that's not right. Yes he is pushy and probing, and he shouldn't be. But you know he's going to do it, and you don't like it. So your only option is to just tell your daughter that "Mommy has stuff to do" and leave it at that. Your daughter is a child and she should be focused on a child's life - not the job of keeping track of her parents and what they are doing and whether the other knows what's going on. Whether you expect her to do this or not isn't the point. The point is, she's doing it!
If you want to be flexible with a visitation agreement, that's fine. But that means for certain occasions, not for your ex to be coming over every night and not for you to re-negotiate every single time there's something going on. That puts you and your ex on the level of discussing who has what plans and which ones are most important for your daughter to be a part of. If you don't want him in your business, then you don't share it. Once in a while, if you have something really really special and you want to swap out some dates, then you negotiate. But your problem with him is boundaries - so you have to establish some.
Moreover, your daughter is in school and has homework (or will have homework), and you and your ex are doing her a huge disservice by not having her on a schedule with her father. This is going to blow up in both your faces when he gets bent out of shape because she has work to do, and she's in the habit over a few years of having her father there every evening. She's going to be close to not understanding divorce - she thinks Daddy comes 'home" every evening - just like every kid with married parents whose dad works long hours. She will not see her father as a separate person with a separate life and a separate home.
If your visitation agreement is not specific enough, then have your lawyer rewrite it for your ex's review. Again, it would be nice if your ex would participate. But if he doesn't, the responsibility falls to you.