I did my Leaving Cert a few years ago and I've now finished my first degree in the UK! I applied to Edinburgh at the time as well - great choice.
Obviously Edinburgh is obviously a very high-ranked uni and very difficult to get into coming from any background, so it's difficult to say. I got simlar JC grades to you (AAAAAAABBB) and was predicted AAAAABBB in my Leaving Cert - I believe they've changed the grading system since I sat my LC, but for context that would be a minimum of 550 points. Edinburgh did, unfortunately, reject me. However, there are so many different factors that go into your application that you really shouldn't let that dissuade you.
They won't ask for your test results since then, but they will ask your teachers to predict your grades. It's worth talking to your teachers beforehand to make sure they're willing to predict a high grade for you - if they know what you're capable of, then your class report cards won't matter as the university won't know anything your teachers don't choose to tell them (so, for example, if you did really well in the summer exam for your chosen subject then that could be worth mentioning, but if you underperformed in one text for an unrelated subject it really won't matter and they'll never know). It's also true that they take grades into account more than the CAO does, but there's a reason for that - they care more about how you do in your chosen subject and related subjects than they do your unrelated subjects. So, for example, all my UCAS offers gave me grades that I needed to achieve but they also had to be in particular subjects - so, for example, I was asked by one uni to achieve AAABBB, but only if two of the A's were in Chemistry (my chosen subject) and another related subject (Physics, Maths or Applied Maths in my case). So, hence the emphasis on grades.
I'm sure you're aware that you'll also have to get your teacher to write you a reference, and you have to write a personal statement. These are really important. I recommend reading lots of personal statements that are available online to give yourself a better idea of what's expected - you don't want to put yourself at a disadvantage next to students from the UK who have such advice more readily available to them. (I was complimented on my PS in particular, though, so I don't imagine it makes that much of a difference as long as you do have an idea of what to write.)
Having said I was rejected myself, I do have some good news! Your predicted results are obviously a little better than mine and, more importantly, every student is different and students predicted similar grades won't necessarily get the same result. It's not like the CAO where points are the only differentiating factor - your personal statement really gives you the chance to sell yourself. I didn't get into Edinburgh but I did get offers from most of my UCAS choices, including some in Scotland, and also from one English university in particular which ranked far above Edinburgh at the time, which shows how unpredictable the process can be. Whether or not you get an offer can be very difficult to predict based on grades alone but your predicted grades are very, very good and it is more than worth a shot.
I'm basically rambling now so if you do have any questions for someone who's been through the process my inbox is always open, but in short: absolutely, apply. The only way to guarantee you won't get in is not to!
As for grants/loans, in my experience I was given the opportunity to apply either as an EU student or a UK student (I have dual nationality) and I was told at the time that I'd only be eligible for maintenance loans etc if I applied as a UK national. However, this was several years ago so please don't take my word for that. Student Finance have accounts on TSR, Twitter and Facebook where they're generally very quick to reply (particularly on TSR and Twitter), and very helpful. It's well worth asking them for advice.