1. "The space will cost about EUR45K so surely that will be too low to incur stamp duty."
I hope you are right, and come to think of it, you just might be. I haven't had to buy a parking space as a stand-alone transaction, so I haven't had to check the Revenue position, but it will be exempt from Stamp Duty if Revenue agree that the parking space comes within the definition of "residential property". Perhaps they will (and there is a certain logic to this - after all it would clearly be residential property if bought along with an apartment). However, it would be best to double check.
2. "Are you saying that re-mortgaging incurs stamp duty?" No, but it might (if total loan is over €254k). However it is only at a rate of €1 per '000.