It's a big city, and like all big cities there is some crime. However, Manchester is really no worse than any other UK city (and the UK isn't exactly crime ridden compared to most nations worldwide either).
If you follow the basic precautions that you would follow anywhere else (e.g. don't walk home alone at night when you're drunk and lock your front door) and avoid making yourself a target, then you're highly unlikely to have any problems. I'm a rather short female and I spent three years in Manchester as a student but I was never the victim of crime.
With regards to your ethnicity, Manchester is a very multicultural city. It's not clear from your post if you're south or east Asian, but there are large populations of both south and east Asians living locally. Just to the south of the university (and on the way to most of the halls) is the famous Curry Mile, which houses a wide variety of South Asian and Middle Eastern businesses. Rusholme (the neighbourhood where the Curry Mile is located) has a very large South Asian and Muslim population. Just north of the university, towards the city centre, is the largest Chinatown in the UK outside London. There's also a very large Chinese population within the university - IIRC a quarter of the university's students are internationals, and of those about a quarter are Chinese. In short - your ethnicity won't be an issue, as you will very much blend in.