Firstly, to confirm, is 'input' the sender/spender and 'output' the receiver of the bitcoins?
Correct.
Is the link above ONE transaction, i.e. when a person pays x BTCs from his wallet to another wallet?
Yes.
If so, why are there multiple ins and outs?
The sender uses Bitcoins from different addresses. Compare it to paying in cash: you give a $20, a $10 and a $1 bill.
One transaction can pay to more than one address. In this case, there are 2 outputs, so it's likely one of them is a change address owned by the sender. In dollar terms: think of it as getting a nickel back.
Is the 'hash' (also in the URL) basically the 'transaction reference (or number)' so to speak?
Yes.
Is the fee (0.00105 BTC in the example) always paid by and deducted from the sender?
Yes. Note that this fee was much higher than needed for this transaction.