I think the names come from Cowboy Bebop more than Full Metal Alchemist :)
Could be...but there is an Edward in FMA who is hot headed and hates being called short. I've come to know many corgis named after FMA characters, especially Winrys. I don't think Tina ever answered the question, so we may never know!
We may never know, it will forever be a mystery :)
I think it's all in the corgis personality itself. Roxi has always been independent and she's about 7 now. She is just starting to get really really cuddly with us. She used to be her own dog though and even if we had her on the couch/lap she would wiggle and just not settle ever. Charlie on the other hand is my couch potato/snuggle buddy so it just all depends on them.