I tend to think of these as having two seperate meanings. If you use 'play with' to talk about a person you are using it's literal meaning (to engage in a game with that person.) If you use the same meaning with an object and the object is a toy, then the same meaning remains. However if you use 'play with' in relation to a non-toy item, you mean to mess around with it and with children it's considered mildly 'naughty' behaviour. 'Toy with' tends to carry the same meaning but for people. 'Don't toy with your sister' means 'don't tease her and annoy her.' That said, 'toy with' is also not that commen in the average person's vocabulary (at least in England.) I think we'd be more likely to say 'don't tease your sister,' or if we are talking about adults, not children, we might say 'don't mess with me.' We wouldn't generally say 'don't toy with me.' Hope that helps!

To toy with and to play with are essentially the same, so yes they can be used interchangeably. I'm personally more likely to use "play", though.

Yes they are essentially the same because when we think of toys, they are used for playing. You could even say they are synonymous to each other.