My first answer would be...it doesn't matter too much.
By that I mean that there is allot of advice that could be given and different options, but for the most part I don't think the child's development or growth is going to be drastically changed by any of these options, so long as camera is not used to invade an expectation or privacy, leaving it running when he is 8 or something (see below).
Having said that here is my general advice, make of it what you will.
First, I would tell him about what your doing now in as much detail as he can understand, and continue to reference the camera often enough that he grows use to the idea, for a few reasons.
- It may get him interested in technology to see cool stuff you do. In general it's a good conceptual concept for him to master, that the camera can make it possible for you to understand things not in front of you etc. In short, it's a learning opportunity and curiosity that is always good to have.
- It's better he doesn't think you have the magic ability to see through walls. Rather then him coming to unreasonable conclusions about your abilities best to set him up with a firm understanding with how the real world actually works. This will avoid a mis-assumption he needs to correct when he is a little older and perhaps keep him more curious about the world if he knows there are answers to curiosities like "how did mom know that!?" maybe he will be more likely to seek them out. Plus, while absurdly unlikely, we wouldn't want him to one day expect you to be watching him through walls when you can't and be either upset that you didn't absorb something he expects you to or worried your see something he doesn't want you to see.
- You can start both setting privacy boundaries and controlling his involvement with you by telling him when the camera is on or off.
The third option is the big one I would focus on. Sure at 2 he doesn't really have an expectation of privacy, particularly when in his playroom; but that expectation needs to develop. You don't want him at age 4 to think your still watching him when he uses the restroom (yes an exaggeration here, but you get the point). Since at some point your need to define this boundary I think the easiest way is to make it explicit from day one, long before it matters, so it doesn't become an issue when it does start to matter.
Tell him he can go play in his playroom and your turn on the camera, but also let him know that you turn it off when he comes out for lunch or before bed etc. You don't really need to stress when it goes off, just tell him when it turns on and he will figure out that must mean it's off otherwise.
This sets early on the expectation of privacy, that your only watching when you tell him your watching, and that the room is still his and private other times.
As an added bonus by telling him your watching at some times he may feel more involved with you even when your busy out in the kitchen. He can say "mommy look" and hold up something he drew to the camera and you can look at it. He can know your watching him build that big tower etc. By making it clear when you are watching he may still get a bit of the advantage of "social time" with his parents even while in a different room; particularly if you talk some while he is in his room. Perhaps even throw in a baby monitor so you can easier talk with him without shouting. This could be a good way to keep him feeling like your involved even when you need to do other things.
I do think that the expectation of privacy aspect is important though. Yes your child is still really young, but ground rules early are easier to grow into. If he learns that the camera is off unless otherwise told now, when he is too young to care if your watching, then by the time he is a little older and just beginning to get a feel for a desire for privacy you can have the camera without imposing on that development.
While even less of a "must do" then the rest I personally would remove it sooner rather then later. At his current age being able to keep an eye on him is nice. However, as he gets older you can safely leave him to run around the house without feeling the need to keep an eye on him. As soon as you find yourself not feeling the need/desire to watch the camera I would remove it, since it's not needed.
In fact I would go so far as to consider making that something of an idea/option for him. Tell him he is a big boy and you don't think you need the camera any more, does he want you to remove it. Maybe he will come to value being able to play in his room and still have you around to interact with and will want to keep it. More likely by the time your ready to remove it he will have no qualm with it going; but you can use it as a "your a big boy, we don't need to watch you because we trust you" moment anyways. I like to give kids these moments of reminding them they are getting older and more responsible, it makes them feel good. You can even tie it in with "now were trusting you, make sure you earn that trust by being good" or something along those lines; so long as you don't make a threat of adding the camera back in if their not good lightly.
You asked about impact of 'spying', which I didn't address yet. First, at age 2 there is little impact. At this age the children expect you to be omnipotent so your being a little closer to that ideal then most isn't going to do any real harm, At most it risks confirming the child's elevated views of your knowing everything which could cause some minor confusion; thus my second point about avoiding such unrealistic expectations, but this isn't too major. I don't think it does much harm right now.
Having said that, I don't think it does a massive amount of good either, unless the child likes interacting with you through the camera once he knows about you. In general he is unlikely to do anything truly dangerous without your being aware of it even without the camera, most parent's dont have it and kids don't seem to be setting fires or anything. Mostly what you would be stopping is annoyances, like his making messes you would need to clean up or breaking something by mistake; and even that won't happen most of the time.
In terms of stopping annoyances, that's nice for you. However, some mistakes are best made to learn from them. If he makes a mess and only later gets yelled at to clean it up; well that can be as much of a learning oppertunity as being warned not to make the mess to start with, possible even more of one since it let him make a decision and then see direct consequences from it rather then having the decision made ahead of time.
In the end I think it all evens out. The camera is mostly about the parents peace of mind of knowing for certain the child isn't getting in trouble, and stopping trouble they don't want to clean up. It doesn't do much harm to not have it, but it doesn't do much harm to have it either, so it seems the covenience of catching a few of those messes ahead of time and, more significantly, your own peace of mind of knowing he is fine when he was suspiciously quite for awhile, is worth having.
What age to remove it is a little more complicated, since this gets into emotional development in many ways. I would say the moment he starts to dislike the camera; not in a "mommy just caught me being bad" way but in a more general "do I really need that?" sort of way it may be time to get rid of it. I'm personally a believer that kids are more capable then we often give them credit for and as such should be given more freedom to make decisions and learn from their mistakes. As such I personally would err on the side of removing the camera sooner, to give a child freedom. This is actually less about privacy, and more of...agency? Giving the child an oppertunity to feel they can make their own decisions, and mistakes, without their expecting their parents to be watching them and fixing everything.
Having said that there is allot of flexibility here in terms of age. besides, as I alrady said, I think the difference is pretty minor either way. Rather then giving you a set age I would say it's time to seriously consider removing when
- the child expresses a wish to stop using it, other then when he is clearly about to do something he knows is wrong and doesn't want caught.
- You find yourself no longer needing it or looking at it.
- The child reaches the age where he starts to be sensitive about being seen naked or his "private parts" (this likely will happen later then the rest).
- You want to teach him a sense of independence or privacy and it makes a good object lessen.
- He starts to actively try to avoid the camera or hide from it at all regularly, even if it's because he is being bad. If he is aware of it enough to be hiding from it he is aware enough to understand privacy expectations and thus desire them.