This is really interesting. It's hard to realize how much of language is colloquial until seeing something like this. The answers to your questions are below.
1. 【cup is half full】 There's a saying about being optimistic where we say that people who are optimistic see the glass as "half full." People who are pessimistic see the glass as "half empty." The glass (or cup) in the metaphor has the same amount of liquid in it, but depending on the person's perspective, they'll see it differently. I think in this scene there's maybe a double meaning because I think he might have been actually drinking a glass a wine that was half full.
2. 【'I got boned at the Museum of Natural History' mug】"Got boned" or "boning" is indeed a slang term for sex. That is the meaning here. I don't know the rest of the context of the conversation so I assume she's making some kind of joke or perhaps a reference to something else. Maybe the mug actually has this written on it. If so, it was probably some kind of gag gift.
3.【now that】. "Now that I think about it" is a set phrase that includes both "now" and "that." It would sound a little strange to say "now I think about it" since the former is a set phrase. We us this when discussing something that we hadn't thoughtfully considered previously.
4. 【wasted】and 【bombed】Regular people use the phrases "wasted" and "bombed" to mean drunk. These terms would be used in casual conversation though, not in formal conversation.
5.【dumpster】A dumpster is a large trash receptacle that usually sits in an alley behind a building. The person is making a joke that he was so drunk that he woke up in a trash bin. The suggestion is that no one knowingly sleep in a trash bin, so someone would have to be REALLY drunk to wake up in dumpster.