Yes, all true but still a mediocre senator from Massachusetts! Senator from January 3, 1953 – December 22, 1960 I didn’t check the election dates but if he was in his 2nd term, he was days into his second term. Again, very Zero like in senatorial performance & presidential ambition!
Both Kennedy and Nixon were first elected to the House in the 1946 election. Kennedy made a point of that in 1960 because he was 4 years younger than Nixon (so that voters would be less likely to hold his age against him).