there is a remote way to recover the Key using the signed transaction made off line in Myetherwallet?
You can safely broadcast a signed transaction as it does not include the private key. Just be sure that you only export the transaction. However this transaction should be written by hand because USB Flash drives and storage media after all can get infected. Or use a scanner.
There is no way of deriving a private key from public key or transaction hash known for now.
I MADE A MISTAKE
I have filled both addresses (address from sending coins, and address to send the coins to) IN THE ON LINE myether wallet, I HAVE PUT BOTH ADDRESSes IN THE ONLINE FORM of MYETHERWALLET.COM
Then I tried to send the transaction, but the nounce wasn't set properly, so it said to me ''Try to adjust the nounce''
So I have put ''100'' as nounce
and the transaction went trouht
it said to me: ''The transaction has been broadcast to the network. That does not mean it will be mined or sent..'' and so on
I am worried.... I just checked on Ether scan and my tokens did not move to the address... they are in my old address... so why it said to me ''the transaction has been broadcastes''?
I am also worried about the mistake of putting BOTH ADDRESSES (the one to send coins to, and the one to send the coins from) IN THE ON LINE MYETHERWALLET FORM OF THE WEBSITE
WHo mined this transaction?
Why it says it has been ''broadcasted''?
Can an attackker with 1 address, and second address + the SIGNED transaction recover my private key?