I initiated a transfer of 0.49 BTC at 2010 hours (GMT) on 01/02/2016 to 1AjFVtmaGSg3rwoSiRRVR6RzQzytyQVWDi
I clicked the recommended transaction fee:
I was not trying to be cheap but the recommended fee for a fast transfer came out as 0.00001130 BTC and I was not able to choose a higher fee and so I sent the BTC.
TxID: 410be500d42a2e8e57bfbc8ed6da06858cd7d81f6218581eaded0f35cd98d78d
Now it's 2 hours later and numerous blocks and the transaction is still unconfirmed.
Well, as you can see in that picture, it says "Smart fee not initialized yet". That means that the estimated fee is not very accurate so you should have set the fee manually. Since the fee for the transaction is low, it won't be confirmed soon. You have a few options. You can attempt an RBF transaction which simply sends the transaction again but with a higher fee. Or you can try a CPFP transaction where you send another transaction that spends from one of the outputs of this transaction. That new transaction will have a high fee, high enough to cover both transactions. Or you can just wait for it to either become confirmed or drop from the network. If it drops from the network, you can send again with a higher fee.
Is there any way to estimate how long it will take for it to be confirmed? A transaction "matures" right? in the sense that it gains a higher priority as times goes on. Is there a way to monitor this or is there a way to cancel the transaction as it is still unconfirmed?
Nope and nope. There is no way to estimate how long it will take as there are many different variables.
There is nothing that makes a transaction "gain priority" the longer it is unconfirmed. There is nothing that does that and that idea is completely false.
