My son's birthday is October 21 and there was almost always snow on the ground in Anchorage by then. I believe the "average" first sticking snow on the flats (as opposed to the Hillside area of town) is October 16. Of course what "average" means these days is anybody's guess.

I'd imagine there are some (very) late silver salmon here and there around then, but they'd be hard to access and you'd have pretty cold feet by the time they're landed. Apart from the stocked lakes in town, I'm sure there're still wild trout and Dollys to be caught, but again, accessing them might be dicey.

By a "day trip" to Fairbanks I assume you mean flying? And a drive to Whittier is always nice, but weather and daylight can become an issue, especially around then when conditions in Whittier can be fairly miserable. As far as "other things" to do is concerned, a lot of it will be weather dependent. I'd check to see if the Alyeska tram is working at Girdwood - you might be caught in the "in-between" period between summer access and skiing, but if it's available it's terrific. Also if there's any fall color left, Mirror Lake (at Mile 23.6 of the Glenn Hwy) can be spectacular; or a visit to the Eklutna village cemetery with its colorful "spirit houses" over the graves is also fascinating. It's at Mile 26.5. I'd be surprised if the Hatcher Pass road is fully open to cars without traction equipment (studs or chains) but it can also be terrific in the fall. Snow's likely, however.

I can't comment on cellular coverage. I use AT&T and haven't had big problems but I haven't tried all that much outside the Anchorage bowl.

Edited to add, if the day trip to Fairbanks is just for recreation, maybe give a thought to swapping Kotzebue instead. The airfare is a hundred bucks more (but it's a good use of Alaska miles) and you'd be able to cross the arctic circle, visit a native community, and stand on the edge of (an inlet of) the Arctic Ocean. There are a couple of flights a day, and there still will be enough daylight in mid-late October to make it worth your while. Just a thought, anyway.