(1) How is it possible to send ERC20 Tokens without gas?
Gas is something like a fuel which must be specified for each and every transaction to take place in the ethereum blockchain. Does your vehicle run without fuel? It is not really possible to send a transaction without gas. What you can set is the price of each gas unit! This may range from 0.1 gwei to how much ever you need.
There are decentralized exchanges which use tokens as tx fee instead of ethereum. For such tx to occur you don't need to have Eth in your wallet. The exchanges withdraw the fee from the tokens you are trying to transfer.
1- the gas price is not zero (0.000000), but something so low that etherscan consider as zero, such as 0.00000001 eth .
Yes that's true, you can specify the gas price as low as 1-10 wei which might be confirmed by the miner after few hours. 1-10 wei is so small that would be equivalent to $0.0001 which etherscan would have rounded off to $0. With eth price being as low as $100 the price of the tx would be considered negligible if we specify it in wei.