The fee was set at a minimum level of 0.0001 as it is for testing purposes only (actually it's impossible to "spam" with Multibit owing to it requires to set the fee at least at a minimum level). I don't know why it was not accepted by the network.
A fee of
BTC0.0001 is the bare minimum that is acceptable, and is likely to take much longer to confirm than the "standard" fee of
BTC0.0005. Though that doesn't explain why it never appeared on the network in the first place. I'm sorry to say I'm out of ideas. Hopefully someone who knows more about Multibit than I do can tell you what to do about this transaction.
The other thing that brought my attention is the way "change" works with Multibit. As far as I understand every transaction decreases "Available to spend" amount to 0 (zero) until the transaction is confirmed in the blockchain- which usually takes about 1 hour. Correct?
Not
every transaction - just transactions that require all the outputs in your wallet to make. Say someone sends you two payments of
BTC5, and then you want to pay
BTC4 to someone else, your wallet would send one of the two
BTC5 outputs, leaving you with the other
BTC5 still spendable (which will increase to
BTC6 once the change confirms). But if you wanted to send
BTC6, you wouldn't be able to do it using only one of the two outputs, you'd have to spend both of them at once, leaving you with nothing until the change confirms. Your initial transaction required all of your outputs simply because there was only one available. Once you have several payments coming in to your wallet, you should never have a problem with your available balance dropping to zero, unless you're spending your entire balance or close to it.