Catholic ceremony

You'd really need to ask your priest. Different churches have different rules in that regard.

You definitely need to ask your priest. My priest didn’t verbally tell us anything, but there was a general reminder in the wedding packet to keep attire more modest. I come from a large Catholic family, and in all the weddings I’ve been to, all the brides have worn some sort of strap, whether they were lace ones or spaghetti straps (mine were spaghetti). No one has worn a sleeve (yet) but I think it’s more important to make sure you’re staying respectful in the church with a dress that doesn’t overly show your bust or have full-on bare back.

My priest didn't say anything. I'm wearing a spaghetti strap dress with a low back. I'm really not worried about it. The veil will help "cover" in a way too.

I would ask the priest or parish wedding contact (if there is one) if there are dress guidelines. There may not be; from what I recall, no one asked anything about my dress or mentioned guidelines. As a PP mentioned, you could always wear a longer veil to cover the back.

Definitely contact your church coordinator or whoever you are working with. I'm also Catholic (though not super practicing as I used to be) and also getting married in a Catholic Church and my understanding (after I asked) was if you feel it won't be appropriate for church use a little cover-up or shawl. My dress is long sleeved but sheer and sheer back so I'm also going with the veil covering me and also my hair.

As for your tattoos; I really don't see why this day and age that should be a problem (even for as traditional as Catholics are) but ask your priest or church coordinator.