How well should a fresh graduate know a language?
There is no good answer to that. It depends on the employer ... and the other graduates you are competing against for jobs.
Some employers of new graduates are looking for people who can start to be productive (at least with simple tasks, with supervision, etc) from day one. For those employers, you should be aiming to get your skills to a level where you can do that, and that you can convince your employer that you have that level in the interview. If you have better skills than the next guy, you have a better chance than the next guy.
On the other hand, some employers of new graduates are looking for people who are smart and hard working; i.e. people who are likely to learn fast. For that kind of employer, good marks ... and signs of a passion for IT ... are more important than specific skills. Deep knowledge of a particular language could be a green light, but if you gained that knowledge at the expense of skimping on your other subjects and got low marks, that could be a red light.
P.S. I feel uneasy to learn just one technology to perfection, because it's limiting my further possibilities.
There's no worry that you will learn any technology "to perfection" ... or even remotely close to it :-)