Oh young padawan, welcome to the EI ecosystem with all its lumbering tech debt and all that entails, all the while its IAG parent adheres strictly to its penny wise and pound foolish strategy of avoiding any capital spending if it can, but building up that UK/EU-261 accrual in the cave of service failure.

Anyway I'll try to address your concerns one by one:

1. EI releases 1 to 2 J seats per flight, I believe 330 days out (open to correction on this) and then may drop some more depending on how J is selling. Unsurprisingly you may find that NYC area airports are quite popular O&D ports for both New York and Dublin, attendant to that is people living in these cities tend to have a lot of cash which they spend on J thus further reducing award availability.
2. Avios.com is a function of IAG acquiring EI and not really wanting/caring to properly integrate it into the Avios ecosystem so you end up with that site the way it is. Some might say that's a feature rather than a bug in the eyes of IAG, make redemptions difficult, you might push people into revenue flights. Anyways, I digress - clear your cookies frequently, use incognito tabs and you'll get it to work.
3. In order to combine Avios your addresses and details need to be exactly the same. Not just close. Exact. #100 instead of Apt 100 will cause it to fail. Double check that & if you're confident all your details are exactly the same & it still doesn't work, you're going to have to call them.

I'm far from an Aer Lingus apologist on here, but the majority of the issues you're encountering are pushed down from the parent IAG and their puppet Embleton, formerly of your beloved BA.