When I make a linked input channel group, can I set an offset in level?
With M7CL, no, you can't keep an offset on the faders, but you could use the Attenuator to keep a level offset between the channels. Keep in mind that the Attenuator is part of the EQ parameters. In this case, you should not link the EQ on those channels. EQ should be disengaged within the Channel Link Mode window.
On the other hand, LS9 can keep offset on the faders. (Owner's Manual p.125)
"You can temporarily exclude a channel from link groups in order to adjust parameters that maintain their level balance while linked, such as when you want to adjust the level balance between channels in a link group. Hold down the [SEL] key of the channel whose balance you want to adjust, and edit the desired parameter. HA GAIN and fader will not be linked while you are holding down the [SEL] key. (However, this function will not work during the fade of a scene memory recall operation.)"