Is it normal for the car to vibrate on the biting point when no gas is given?
When I give enough gas it seems fine but not when I very slowly release the clutch and hold at the biting point. Is this an issue?
More than likely, the clutch just isn't broken in yet (or bedded, for that matter). You need to not ride the clutch at all, don't over heat it, and don't try not to prolong it's usage during this period. It's common for a clutch to have some small amount of jidder while in this phase, so don't be surprised. Once it becomes evenly worn and broken in, you'll probably notice the bite becomes much smoother. Don't expect this to happen until around a 1000 miles or so.
This is perfectly normal and there is nothing wrong with the car.
Think about what's happening.
You're transitioning the car from an idling engine that's turning with no load on it, to one that's supposed to be turning the wheels. Specifically, it's supposed to be turning the wheels at a rate proportional to the minimum speed of the engine (via whatever gear). It's especially difficult for it to do that when setting off, because the wheels aren't currently turning at all.
In other words, you're adding a lot of resistance to the engine. If you take this to its conclusion, you will stall the engine, which is you reducing the engine speed to below the minimum. As you've no doubt experienced, this makes the car shudder.
Instead, you avoid the stall by either adding more fuel to overcome the resistance, or by taking the resistance away, i.e. depressing the clutch. In your case you need to do more of the former.
So, don't try and set off without any throttle. You'll wear the clutch and add load to your engine.