My wallet does not show me the right balance of tokens
The MyEtherWallet node was under a lot of strain and it is advised to switch node in the top right. If you're just looking at your balances, use a block explorer so you don't expose your private keys.
When trying to send those tokens to another Ethereum address (that I specify), what is broadcasted to the blockchain is a tx to a different address...
This is because you make a transaction to the contract address and invoke a function
transfer() which takes 2 parameters (the amount of tokens to transfer and the address to transfer to).
Function: transfer(address _to, uint256 _value) ***
The above tells the contract to transfer KC tokens to address 0x280c699961D44592C1655be22C272B4c0cFc4a06.
"Transaction execution error"
This is a report that the transaction failed to complete - see below.
Warning! Error encountered during contract execution [Bad instruction]
This is because a condition in the contract did something to kill execution. Without reading the contract, I'm unsure what that is.