Hi Hadi
Living in Chester is usually a lot less expensive than living somewhere like London. Like any place, there are some expensive lodgings and some cheaper ones. You have to investigate before signing up for any rental contract. The University probably has a list of approved landlords and landladys.
It's a lovely little city. It has usually been a busy one too, since the days of the Roman Empire!
There should be scope for part time work. There are many pubs, hotels, bars etc. It is a major tourist city in the North West. You just have to be flexible in the kinds of part time you can do. Also check out the wage rates.
Regards
Angelette 8-)