Floating atop of water, ice is a great deal more supported and hence, stronger, than in a freestanding wall. How strong depends on the type of ice, but you probably want to be careful if attempting a similar feat in real life, as falling ice chunks can be very heavy and it's pretty easy to hurt yourself. A little bit like punching through glass. It can be done, but it might end really badly if incautious.
That wouldn't break my suspension of disbelief, I think. Yeah, it's certainly an indication that she is strong, but Tolkien's elves have not generally been portrayed as weak. It's a feat, but not one that is greatly outside of human capacity.
I'm not super interested in the show, but something like this won't bother me unless it somehow undermines something important.