Does anyone know whether one needs to pay a fee of 1 ANS when sending ANS to their address for claiming ANC?
Bittrex charges 1 ANS/NEO currently. The new Binance exchange on which ANS/NEO will be listed will certainly not do that. Bittrex will likely change its fee when it gets more competition from other exchanges listing ANS/BITTREX. If you are not using Bittrex, then the fee does not apply.
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So what is the consensus mechanism, PoW or PoS or hybird??
It does not use either. It uses the Byzantine Fault Tolerance (dBFT).