No - Jerusalem is the official capital of Israel. Tel Aviv was the temporary capital of the state of Israel for a short period between 1948 to 1949. The Knesset was moved to Jerusalem in December...
The current Mayor of Tel Aviv, Israel is Ron Huldai. Huldai was first elected mayor of Tel Aviv in 1998, was re-elected in 2003 with 62% of the vote, and again in 2008 with 50.6%.
As both cities are large, I would say about 55 miles. I ran a calculation in an Israeli map site (see link below), and got 50 miles for two close points, and 60 miles between the two cities' centers.