Forgive my ignorance, but I thought a transaction was not final until it was included in a block that was accepted in the blockchain. I assumed that if there weren't any slots for the transaction, then its finalisation would be delayed.
It is good to ask. I was referring to the person that you've quoted. Your thinking is correct; until the transaction gets included in a single block (1 confirmation) it is marked as a zero-conf transaction and is not final.
It's possible to reverse a transaction with 1 confirmation but that is quite hard and becomes much harder the more confirmations that it has; these are things that you do not need to concern yourself with though. Your assumption is also correct, but mostly for transactions that have an inadequate fee. You could "take" someone else's "slot" by including a fee that is a bit higher.
If blocks are submitted half empty at the moment, why do we need to increase the blocksize to create more empty space/unused capacity?
There is no need for this right now. The fork is an political attempt at taking over the development of the main implementation. Segwit offers an adequate increase in transaction capacity (along with other benefits) and should ensure enough space for 2016 (it will grow with adoption).