Silicone is pretty strong and a larger gap actually allows it to absord more movement. With the backer rod it will sit just nicely.

Grout is water permeable and will actually allow water to leak behind causing damage.

Silicone all the way.

I've done this before. The grout will crack because it's brittle and the shower pan and walls expand and contract at different rates depending on temp and humidity. You need something stretchy like silicone for any transition in surface, even inside corners of the same kind of surface.

Absolutely should NOT be grouted. Never grout a change of plane like this.