When the life of a Sotapanna ends, let's say he/she reincarnates as a human.
Yes, Sotapannas can either come back as devas or humans for seven times at most:
"Again, some person fulfills virtuous behavior but cultivates concentration and wisdom only to a moderate extent. With the utter destruction of three fetters, this person is a seventimes-at-most attainer who, after roaming and wandering on among devas and humans seven times at most, makes an end of suffering. This is the ninth person, passing away with a residue remaining, who is freed from hell, the animal realm, and the sphere of afflicted spirits; freed from the plane of misery, the bad destination, the lower world" ~~ AN 9.12 ~~
Does that mean, the reincarnated is capable of demonstrating the qualities of a Sotapanna since a very young age?
Quite possible. It's like the cases of those music or math prodigies who demonstrate extraordinary potential at very young age. A more concrete example related to the Dhamma was when the Buddha attained the First Jhana when He was a kid!
Or, does it take years of practice (again) to regain Sotapanna qualities ?
Since it's all about potential and capability, it's not that one has to "regain" Sotapanna qualities, but it's just that there're various differnt sub-levels within Sotapanna: some do take the maximum span of 7 lifetimes, some only takes 1 life, etc. So, again, really depending on how much one cultivated in his previous lives that he could either be like a Mozart, or a Chopin, or a Paul Mauriat.
And is there anyway to tell if a kid attained Sotapanna in his/her past life ?
It'd take a Sotapanna himself to really know AND experience firsthand all the Sotapanna's quality, in order to truly tell if someone else is also a Sotapanna. However, just like the attributes of a math prodigy, a Sotapanna kid could show early signs of Dhammic maturity, some natural instinctual tendencies toward virtues, calmness, wisdom( Sila/Samadhi/Panna ) without much coaching or close guidance from his/her parents.