Is there a time limit how long a signed transaction is valid?
Bitcoin is not an account based currency like Ethereum, which track the balance in addresses. Instead it is a UTXO based currency. In a UTXO-based currency, funds are tracked in portions called "Unspent Transaction Outputs", these are uniquely identified through their history, specifically through the transaction id that created them. Any new money moved to the same address would have a different history and thus would not be replayable.