Mining is based on economic incentives. The miners are believed to want to maximize their profits. Therefore because mining a block (finding the right solution to the mining puzzle) is so hard he should include as much transaction to a block as he can because the amount of time processing the extra transactions is insignificant compared to ...
The Gibabyte Gtx 970 provides hashrate of 22 MHash/s for Ethereum at Coreclock 1563 while consuming 185 watts.
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Yes, a new block is validated by all nodes. No, it is not possible for a block with invalid transactions to be part of the main chain.
You can mine a block with an invalid transaction. But all the other miners will ignore it.