AFAIK, Legacy addresses don't contain witness field, or should i say, don't support. so both its signature and pK are placed inside the scriptsig, which is then used to know the tx size and calculate the fees. Unlike the other two type of segwit addresses that has witness field, while their difference in how they push their data makes them distinct from the other. I have once asked why Native SegWit (Bech32) addresses have lower tx fee than SegWit (P2SH), and here is one of the best explanation i got for those that are interested...
Low tx fees - Technical difference between SegWit and Native SegWit addresses?.
Exactly, the misconception has always been that SegWit removes witness from the transaction and therefore reduces the size of the transaction which is total wrong it technically doesn’t do any of that, rather what SegWit does is changing the usual way of calculating the size of the transaction changing from size to weight and then this fork introduces a new field we call the witness, this witness is much smaller in weight than the usual one we have in legacy address format.
So with the transaction fee then now calculated base on virtual size and with SegWit, witness is the new replacement which smaller in size than the usual Legacy it will mean that more transaction of SegWit can fit into a block than Legacy which is why there is lower fees
When you are sending to a similar address, I guess it would be cost free?? Haven't actually transferred out to a different wallet mainly due to fear of loosing my assets.
Don’t get confused, there is no way a transaction will cost free, although technically the bitcoin network doesn’t makes it compulsory that their should be fees, if your wallet client or node accepts, you can send transactions to any address format without fees, but miners prioritize transactions based on fees so wallets have built there clients to actually reject any transaction with fees or even fees below 1sats/vbyte. So realistically it is not possible to send transactions without fees.
As for fees, the choice of address format and the number of input and output affects the amount to be paid for fees, because fees are based on the transaction size