The regular speed audio sounds an awful lot like "un coq et un oiseau". This doesn't apply to the slower audio, which more clearly accentuates the "est"...
"et" and "est" sound exactly the same we can't distinguish them. It depends on the context.
No. Typically, et is /e/ and est is /ɛ/, but the difference is subtle and even so, there should be a liaison with the "t" in est ("eh-T-uh(n) oiseau") but et never makes a liaison.
A warning to non-fluent English speakers.... "Cock" is a very naughty word in American English. Don't use it at all in polite or formal settings, even to refer to a male chicken. Use "rooster" instead.