Is there a way to obtain account historical (for a given block) balance using catapult REST?
There is no such Rest API at this moment afaik.
My suggestion is to join the discord at start discussion around this with team: Official Symbol Discord Channel 
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Thank you, I will join discord. Is it possible to reconstruct balance from transactions 100% reliably? Is there a SDK code for that in any public repo? Or do I need an access to a node?
Each node exposing API:
https://docs.symbolplatform.com/symbol-openapi/v1.0.0/
There are also SDK available: