Thank you very much. Thats very clarifying !
Considering they are on the same blockchain, if "everyone" is using one or the other, there will always be miners working to process the transfer on the "not used" output ?!
So ive always had my bitcoin in my hardware wallet. Now there are 2 options: Legacy and Segwit. Whats the actual difference ?
Legacy means that you will be using addresses of the form 1... Segwit means that you will be using addresses of the 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.
1. Can i transfer my btc from Legacy to Segwit as a normal BTC transfer ?
Yes.
2a. Does it make a different where i hold my bitcoins ?
Yes. When you want to send money, transaction fees for spending a segwit output will likely be lower from spending a legacy output.
2b. Do they use the same hashpower ?
Hashpower and addresses are unrelated. In fact, addresses don't even exist on the network; they are just a human abstraction that tells the wallet what to put in the output script of an output.
3. Considering segwit was activated, why my BTCs are not automatically on the Segwit chain (are there actually 2 chains ?)
No, no there are not two chains. Segwit is activated on the Bitcoin blockchain.
4. Whats my play ?
If you want to use segwit, get some segwit addresses and begin giving them out to people when you want to be paid. You can also make a transaction sending your coins to segwit addresses in your wallet. If you don't want to use segwit, then do nothing. Either way is safe.