I believe they were taken in captivity at Tsarskoe Selo in 1917. The fact the 2nd one is in Anastasia's 1917 album, helps greatly because other wise I would wonder if this was 1916.
I think the two photos at the bridge to Children's Island featuring Alexis ,were taken the same day...and the sunlight tells us, very close in time. The one with the Imp on AP's Circuital Hall terrance ,could have been taken that day as well and very likely was .... But this had to be early on in captivity since Alexi's has his small rifle in the photo with Anastasia and we know that was taken away at some point.
In the first photo, the guard is using a type of pump that seems to be taking canal water and spraying someone off camera with a small hose ...well you KNOW Alexis wants to be in on that...he's climbing the bridge as fast as possible to join the guard and I'm sure, ask to use the hose himself ( on someone of course!) lol! I imagine it was gas powered and just started up and proved it can spray very well lol! AN would have been there from the start if they knew it would work so well imo
I love these photos of course...thanks for posting!