consensus EPS

Firstly what you must understand is that there is no "one" consensus. Consensus is just an average of sell-side analyst inputs. The average is done by a "data collector" (word I just made up), but there are multiple collectors - Bloomberg, Refinitiv, VisibleAlpha, the company themselves etc. Not every collector gets given all or the same inputs or even does the average calculation in the same way (median vs mean vs some sort of "smart average") thus their consensus will be different but normally not significantly so. This is why you can't/shouldn't read into a company beating by +-1% as anything more than an "in-line". Now that that's out your way:

1. Depends. It's normally whatever EPS makes most sense for the company. For some companies it might even be an "operating" EPS. But consensus is collected for all sorts of figures, not just EPS. So it's very likely that there are basic, diluted, operating etc. figures available and thus whatever "EPS" the presenter means depends on who that presenter is. For this specific company, it doesn't matter because basic/diluted are the same.

2. Basically relates to my first paragraph, they all have different sources.

3. Not sure where they're getting 1.77 from. There's potentially a background adjustment they're doing (or not doing) that should be done. I would trust company financials over yahoo finance... However if you actually look at the Financials tab on Yahoo finance, you'll see the EPS is 1.88.