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Tess: Rough night:
Oliver: Yeah. Somewhere between chasing the bad guy and
dodging the press I ran into someone who had an ax to grind.
Tess: That sounds like some serious overtime.
But if I remember correctly, your cure-all was two raw eggs
in a Belgian beer
, (a mixture of them?) hmm?
Oliver: Yeah, let me tell you something, Tess.
I can do this whole 9:00-to-5:00 thing with you, (Tess is his assistant so I get this part) all right?
But I draw the line at Happy Hour. Is that a way for Oliver to say he doesn't need
her criticism as additional service to him?
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1-- Yes, a mixture. Hair of the dog.
2-- I don't think so; he is just saying that he doesn't want to go out with her after work.
Comments  
Students: Are you brave enough to let our tutors analyse your pronunciation?
After some time Oliver shows up with a six pack.
Tess: I thought you said no happy hour.
Oliver: Yeah, but I'm still on the clock, (nine-to-five?) so...
Happy Hour is a custom, at least in the U.S., I'm not sure about Canada or Britain, where drinks are sold at discounted prices for a certain period of time, (sometimes more than an hour, although it is called happy HOUR, it sometimes lasts 2 or more) right after most people get off work. It would be a common thing to say, "Would you like to join us for Happy Hour at Bennigans (a restaurant and bar)?"

Or, just, "We're doing Happy Hour at Bennigans. Want to join us?"

So, as MM said, he was telling her he would work with her from 9 to 5, but wouldn't be going out with her after work. Happy hour has become a slang expression for going out after work, where you might or might not find discounted drinks at your favorite watering hole.

You might say about a comrade at work, whom you get along with well enough there, but don't want to become a social friend with outside of work, "He wants to do the whole happy hour thing, but I'm just not into that when it comes to him."

Dropping raw eggs into beer, sometimes with a shot of whiskey, as well, is, as MM alluded to, a "cure" some use for hangovers. The act of drinking more alcohol to make a hangover less painful is called, in a slang expression, "having a hair of the dog that bit you," ergo, his reference to "hair of the dog."
Thanks, Mister Micawber and sam1947!
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