Trek in Ile-Alatau mountains -permit ?

[Soph]

Hello !

We'd like to do the Shymbulak - Big Almaty lake trek though Tourist pass in 1 week, and have several questions about it.
https://x-travels.ru/gornye-poxody/bols ... e_vignette

- is the zone accessible without a permit ? We read that access to Shymbulak or the Big Almaty lake are allowed, but it is okay to trek in the other parts of the national park ?
- is the itinerary doable in lat April ? (Snow, bad weather, avalanches, ...)

Thank you very much in advance