Morning,
I'm based in Kazakhstan on a Corporate Jet. ATC usually efficient and safe (Almaty based). They are used to Western Europe crews - its fairly hassle free. QNH available - if you ask! MSA just south of the Airfield goes vertical..
Weather this time of the year in Almaty & Astana grim - Astana significantly colder than UAAA, -26C the other day, taxiways and ramp like a Dutch Skaters worst nightmare.
TAF's nearly always VV001 due to the metmen getting in trouble if they get the forecast wrong - so it always looks bad! We 'tanker' fuel so we have as many options as possible for Div, Bishkek & Astana usual for Almaty. KZK is a VAST country, look long and hard at where you will go if/when the Destination goes out in weather.
Bek Air FBO in Almaty OK, they will sort most problems out at the airfield, then get you away to the Hotac (Hyatt where most Bizjet guys go, though Holiday Inn OK). Make sure you get a Gendec stamped inbound by the Customs Guys in the HUGE hats - helps on the escape plan!
Dont know anything about the CJ1 - but read up on Winter Ops and what you need to do to protect the Jet overnight, draining water, battery removal etc.. De-Ice at UAAA fairly efficient, but you need to pre-book then make sure you keep hold of the handler, once he vapourises for a coffee you will be alone. Security on the Airfield good, almost too good, getting out of the country can be tricky if Visa's are not exactly right.
Good luck!