Your answer can be found here: http://en.wikipedia.org/wiki/List_of_Hot_100_number-one_singles_of_1995_(U.S.)
The #1 single on the Billboard Hot 100 on 19 Oct 1995 was Fantasy by Mariah Carey.
On the week of February 28, 1995, the number one song in the United States was 'Take a Bow' by Madonna. It held the number one spot for seven weeks.
Lady Kenny Rodgers
enakedladies
The electric slide
because of you
I'm assuming by the wording of the sentence that the song was titled "One Week". That would've been the Barenaked Ladies.
Apollo 10 was launched May 26, 1969. That week, the number one song in the U.S. was "Get Back" by the Beatles. The week prior to launch, the number 1 song was "Aquarius/Let the Sunshine In" by The 5th Dimension
Saturday, the day before my sister was born!
Get Back by The Beatles
Running Bear
The longest running number one song was One Sweet Day by Mariah Carey and Boyz II Men. This song was number one for 16 week in 1995.