RBF is does not seem to be available as there is no transaction for this request showing in History and when I double click the date section where it says Pending, nothing happens. The coins are still sitting in my Electrum wallet and there are 0 transactions recorded on Blockchain.info so my question is this: if the transaction never gets confirmed and drops out of the mempool, will Pending change to something else, i.e. unconfirmed or unsuccessful, thereby allowing me to resent the transactions with the appropriate fees?
Try right clicking and see if there are any options to bump fee. If it gets dropped from the mempool, the UTXO would be as if it was never spent.
If it really does have no fee at all, its quite likely that the propagation was terrible. You could consider removing the transaction and sending another one. It could work without RBF too.
Also, do all transactions have to have a signature? What happens if they don't?
Pretty much. There are special cases where it doesn't. An example is 3MaB7QVq3k4pQx3BhsvEADgzQonLSBwMdj. Its an example of anyone can spend. It is nonstandard as it doesn't require a signature.