Yes you can do that, offset pins are used to adjust voltage across two nodes in the OPAMP. If you do not connect potentiometer, your circuit will have non zero offset.thats all.
Yes you can do that .....you can keep them floating.....but generally with input bais control is best method to tune the output ....So will recommand you to have the biasing circuit....
In general, yes. There are many circuits using opamps in which an offset of a few millivolts makes no difference. There may be some special opamp types that need to have the offset adj pins connected in a certain way even if they are not used, but offhand I can't think of any.