Did the Gentiles at Cornelius's house have to repent or be baptized to be saved?
No. The Gentiles at Cornelius's house were saved by faith alone. The Holy Spirit fell on them before Peter said anything about repenting or being baptized, evidencing their salvation by faith in Jesus as the Christ. They became believers without an invitation, walking an aisle, repenting, or baptizing.
Les explains that Peter and six other Jewish believers went to the Gentile home of the Roman officer Cornelius. While Peter had not yet finished preaching and had not said a word about repenting and being baptized, the Holy Spirit came down and signified to those seven Jews that these Gentiles had become believers. Without an invitation, without walking an aisle, without repenting, without baptizing, Peter was stopped in his tracks, and these men evidenced their salvation by faith, and faith alone, not yet Paul's gospel, only that Jesus was the Christ.
While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.
And God, which knoweth the hearts, bare them witness, giving them the Holy Ghost, even as he did unto us;
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Did the Gentiles at Cornelius's house get baptized or repent before they received the Holy Spirit?
At Cornelius's house the Holy Spirit came down on the Gentiles while Peter had not even finished preaching and before he said anything about repenting or being baptized.
Were the people in Cornelius's house when the Holy Spirit fell mostly Gentiles or Jews?
When the Holy Spirit fell in Cornelius's house, everyone there was a Gentile except for the few Jewish men who had accompanied Peter from Joppa.