What is the phrase for "sounds like" as in "it sounds like your dad is getting better"? At first I thought I could use 听起来, but if I'm not mistaken this is only used for actual sound, not "you just told me your dad is back from the hospital, it sounds like he's getting better each day". (My version: 听起来你的爸爸越来越好，太棒了！)

What about 看起来? Some of the meanings given by the dictionary are "gives the impression that" and "looks as if", is 看起来 reserved for actual physical appearance or can it be used in the context above?
Drunken (programming) Master is right. These 2 from iciba:

It sounds like a wonderful idea to me, does it really work?

听起来这个主意很不错，真的能行吗？

His rhetoric sounds like the death rattle of a fading leadership.

他的慷慨陈词听起来像是一个衰落的领导层垂死的挣扎。

They also have examples of 听上去。It's a great site for finding example sentences.