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Except for я in endings:
Катя [ˈkatʲæ] vs Кати[ˈkatʲɪ]
дача [ˈdaʨæ] vs дачи [ˈdaʨɪ]

For about unstressed э, i.e. [ɛ] after a hard consonant, after a vowel or at the beginning of a word, it is...

Although iCake says he can distinguish -и and -е in the ending position, and there actually are minor differences in pronunciation in different areas of the country, I believe the standard language...

[...rə]
[r] is hard here.

/e/ and /i/ merge in most unstressed positions (e.g. лиса 'fox' and леса 'forests' are pronounced [lʲɪˈsa]).
Some speakers distinguish /e/ and /i/ in the ending position, though. (звери vs о звере)...