Some four letter words that have two vowels are:
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Place
One seven letter word, One two letter word and a five letter word, One three letter word and a four letter word, One three letter word and two two letter words, Two three letter words, Three two letter words, A two letter word and a four letter word, A six letter word, A two letter word and a three letter word, A five letter word, Two two letter words, A four letter word, A three letter word, or A two letter word.
Blanket, country, dolphin, endless, friends, forward, gravity, harmony, history, hundred, husband and kingdom contain only two vowels. Additional words include lobster, monster, nothing, perfect, problem, pumpkin, respect, seventy, student, whisper and working.
enter
No. In the official Scrabble dictionary there are lots of four-letter words containing two i's, but no three-letter words.