"Falas" always gets me, because it seems so much like "Fala (He/She/It/You speak)" in Portuguese. So I keep answering speaks or talks.
I think that this is the only hard part about Esperanto (And it is REALLY hard to find something to complain about in a language purposely made so easy for us). It's desensitizing yourself to the structures of other languages. Something tells me that português is gonna keep tripping me up, but that's ok. We'll all get it at some point.
The verb renkonti comes from French rencontre. I am starting to like Esperanto.
According to the theory that all Esperanto sounds always sound the same, it should be like "sheen".
However, I hear "shin" a lot as well from speakers of e.g. German or English, where vowels in open and closed syllables (ending in a consonant or not) often sound different.
In USA English it would be pronounced "sheen". Which is what I heard when listening to the examples given by Christian and Nicole_USA. The "i" has the sound of an "e" as in see, be, tea. Sheen has a double "e" that sounds like a single "e". Shin has an "i" that sounds like the "i" in fish, dish, wish.
In nominative-accusative sentences such as English or Esperanto, if you leave off the subject of the second verb, it will be the same as the subject of the first verb.
So "He meets her and falls" = "He meets her and he falls".
(Things would be different if we were talking about an absolutive-ergative language such as Basque or Inuktitut.)