In a nutshell it is an improvement over the current bitcoin blockchain which reduces the size needed to store transactions in a block. This is done by removing certain signature with counting serialised witness data as one unit and core block data as four units.
The name stands for Segregated Witness. Segregate means to separate, and Witnesses are the transaction signatures. Hence, Segregated Witness in short, means to separate transaction signatures.
The increased capacity to store more transactions means lower transaction fee, more transactions per block = faster transactions. In addition to that it would also fixes transaction malleability, an attack that lets a person change a Bitcoin transaction’s unique ID before the transaction is confirmed on the Bitcoin network.
If you have Legacy address then it means that you will be using addresses starting form 1… SegWit address means that you will be using addresses starting form 3… or bc1… (one is for P2SH nested SegWit and the other is for native SegWit). Note that 3… addresses are for P2SH addresses in general and are not just for SegWit. bc1… addresses are for SegWit specifically but not all wallets support it yet.
Yes, SigWit is a soft fork and it is backward compatible.
Yes. When you want to send money, transaction fees for spending a SegWit output will likely be lower from spending a legacy output.
No, there are no two chains. SegWit is activated on the Bitcoin blockchain. It is backward compatible.
SigWit2x stands for SigWit + 2X block size = 2MB. This fork was due to launch in 2017 but later cancelled as not many miners supported this.
If you have more questions, do ask them below, I will try to cover it above.