Using avoir to express should have

Question

I have two separate questions regarding the same example 
The first is…why do you use “sa tête” to mean “his face”? 
The second is…I am sure that there are many colloquial ways or common ways to express “should have” using the verb avoir in its conditional conjugated form when it’s not followed by “dû”, but is it actually proper French grammar? For instance, in one of the above examples, it reads: “Tu aurais vu sa tête quand je suis apparu devant lui.”  Its translation is “You should have seen his face when I appeared in front of him.” Possibly contextually it translates better to should than would. Perhaps if the sentence was “ Tu aurais vu sa tête, si tu avais été là.” Then it’s a true conditional statement-You would have seen his face (condition) if you had been there. So perhaps I’ve answered my question because this really isn’t a conditional statement However, I like rules, I like things to follow those rules (The Container Store is one my happy place-quote from Emily in Paris). I also realize that as I write this, the English language is known for not always following grammatical rules in one sense or another (although I can’t think of any because it makes sense to me as a native English speaker, so please forgive my hypocrisy). Please help me understand when avoir in its conditional form means should when not followed by dû.

Chris Wirt · Accepted Answer

1) Why use sa tête to mean "his face"?
In French, you often use tête when referring to how someone looks, their expression or emotional reaction.
Il a fait une drôle de tête. -- He made a funny face.
 
2) Tu aurais vu sa tête quand je suis apparu. 
The classic conditional would be: Tu aurais vu sa tête si tu avais été là. -- You should have seen his face if you had been there. In the sentence you quote, the conditional is used as an idiomatic exclamatory function. French use of the conditional is a bit looser than the English.