There are no constraints on how the money gets transferred, just as long as the $10k eventually gets deposited in an approved PRA bank.
In principle yes.
Personally I think it's much better that the SRRV is applied for in Manila. It's said to be very smooth and easy with approval being almost certain as long as you've got ALL the documentation needed.
Usually the PRA will organise everything for you at their "One-Stop Shop" such as NBI criminal background check and needed medical exams.
That way at least you won't need to go to the Philippine Embassy to get your documents certified by the Philippine embassy.
To be honest, I'm not sure if the PRA will also insist on Police Clearance from Ireland or not. I would suggest you make contact to ask the question, or even just go ahead and get the Clearance anyway.
As I'm sure you know by now, sometimes it's not easy to give always definitive answers about how things will or will not be done in the Philippines. Often, such things like official decision making can become a bit blurred around the edges being less dominated by regulation and rule and more about situation and personality.