It is always a good sign if you do not hear any noise from an amplifier with the volume at maximum and no source is connected. On the other hand, a slight hiss is not unusual under these circumstances, and I would not be concerned, especially if the hiss is only noticed when you are close to the speaker. Even when heard from the listening position it is probably not that unusual with full volume. It's when you hear noise with the volume at normal listening levels that it can be considered a problem. But it still is probably just inherent circuit noise, and all amplifiers have some noise, though it's not always audible. The music will probably mask any slight noise, but of course it is always best if the electrically generated noise is as low as possible.

A hum when switched to phono input, but without a turntable connected, might be the higher gain phono circuit picking up noise from the power supply.  Probably nothing can be done about it unless it is some kind of correctable grounding issue. Again it might be normal with this amplifier unless it's audible when listening to music.