We crossed into Kazachstan recently using the border between Astrakhan and Atyrau. Yes, you can buy insurance there. Around 20 EUR for 3 weeks if I remember correctly.
In Kyrgyzstan there was no insurance at the border, and we used the major Bishkek border. Nobody asks about it, so I wouldn't bother.
For Uzbekistan I don't know yet. Gonna enter next week.
Cheers
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