It can be on any day of the week. It will depend on the year. As this question was asked in March 2013, then the 7th of April in 2013 was on a Sunday.
That will depend on what day of the week the 1st of April is on. Whatever day of the week it is on, if you are taking the 8th of April as being 7 days later, then it will be on the day of the week after the day of the week of the 1st of April. So, for example, if the 1st of April was on a Saturday, then the 8th of April would be on a Sunday.
April 7 2010 was a Wednesday.
April 7, 1957 was a Sunday.
April 7 1998 was a Tuesday.
7 April 2008 was a Monday.
April 7, 2005 was a Thursday.
April 7, 1995 fell on a Friday.
April 7, 1975 fell on a Monday.
Wednesday
Tuesday
It was on a Wednesday.
Thursday