anyone know what is SDK for TonKeeper Wallet Signing?

this?
https://github.com/tonkeeper/wallet-api

what is a maximum length of string stored in slice?

cells can contain 127 chars, but you can build snake strings

yeh, but I remember TonKeeper enable to pop-up the window to ask people sign the message. (to proof the wallet owner want to log-in etc

i had not an experience developing this kind of apps, sorry

does FunC supports some kind of arrays? i need to store collection of cells in smart contract's storage

FunC supports Tuples - https://docs.ton.org/develop/func/types#tuples-types
You must pack your data into a cell (a tree of cells) in order to store it in storage. You will not be able to write a Tuple in the Contract Storage.

thanks