Which area/district is closed to Seef district?Like 10-15 min by car??

Bahrain is a small place. And most areas are just 10 to 15 minutes away by car

Areas in an around Seef are:
Sanabis
Daih
Karbabad
Manama Souq

The first three areas have minor issues and hence better to avoid these.

But as I said, Bahrain is a small place and most areas are 10 to 15 minutes away any way.

Most of your questions were answered on your previous post.

A private driver will be cheaper than a taxi like Farhaz said, so once you get here ask at your course and people will advise you. There is also the option of car sharing with someone else on the same course.

The rent you were asking on your previous post is very low so you won't get a decent property for a family. More like a studio room. Again like Farhaz said - Google "Bahrain Property World" and take a look. Also Google "map of Bahrain" and take a look, it will give you some good ideas

the rent budget you mentioned is rather low, especially when talking about a place closer to Seef.
you can find decent 1 BR apartment starting from 350~380 BD in Seef surroundings.