Whatever the actual reason for choosing the liver was, we can be certain it wasn't its regenerative property, since such proprerty was unknown to the Greeks at the time.

Probably not, I don't think I ever read Galen mentioning it, but then again people would get injured in the liver and recuperate better than other injuries I suppose, which makes me think it is surprising if he didn't.

Just went and checked, evidently he never said anything about it.

old American translation of Galen and Hippocrates for anyone interested, as it can be difficult to find otherwise

https://oll.libertyfund.org/titles/coxe-the-writings-of-hipp...

And you know because you were there?