Travelling from mainland USA to Alaska

The short answer is "no", but the reason why will depend upon which route you take.

Presuming you take a direct flight from the mainland US to Alaska, then this is a domestic flight - despite the fact that it flies over Canada, and the fact that Alaska is not directly connected to the US. As with all domestic flights, you do not need a valid visa as you are not leaving or entering the US.

If you take a flight that goes via Canada, or if you travel overland such that you exit the US and enter Canada then it's a different story as you will need to re-enter the US - which would normally require a valid visa. However presuming your status (ie, I94) is still valid then you can re-enter the US using a process called automatic revalidation which basically allows your existing status to continue, even thought you left the US for a short period. (Note however that you may require a visa to enter Canada!)

So regardless your path, you are good to travel and return without a valid US visa.

Alaska is a state, not a foreign country (even though sourdoughs may argue differently ;-)

You will not pass through immigration going or coming. All you need is a valid ID to board your flights.