2. I will be in Anchorage for more than one week. Should I rent, buy a bike there, or bring my own bike?
The answer depends on three variables.
Variable I. Do you like the bike you currently own? If yes then depending on which airline you are flying in to Anchorgae on, consider option A.
Option A: If you like the bike you currently own and the airline you are flying on charges the same to check a bicycle box as it does any other piece of luggage, then you should probably bring your bike. Here are three airlines that treat bike boxes the same as regular luggage so long as they are no more than 50 lbs.
Alaska Airlines: First bag - $35. Second bag - $45. Third $150. However there are a number of waivers which could make the first or second bag free and those are listed at the bottom of their Exceptions and Waivers page.
Delta Airlines does not charge extra for bike boxes but it does cost $30 for your first piece of luggage and $40 for the second. Like other airlines, the bike box must not be more than 115 total inches. To confirm, here is a link to their policy: Delta Airlines Baggage.
American Airlines: First bag - $30, second bag - $40, third bag - $150. You may not have to pay however based on you AAdvantage® status or oneworld® status,
United Airlines "[o]versized fees are waived on properly packed bicycles." https://www.united.com/en/us/fly/baggage/sports-equipment.html This means that "The equipment counts toward your checked bag allowance." If you click on may be subject to fees that page states that the weight limit is 50 lbs. (First & Business class passengers can check an oversize bag no more than 70 lbs.) Next, scroll down to "Additional Info" and click on the dropdown menu "Oversized, overweight, and extra bags." Here it explains the maximum dimensions of an oversized bag. "We can’t accept bags that measure (length + width + height) more than 115 inches (292 centimeters)." This is within the maximum dimensions of most cardboard bike boxes but measure first before getting one from your neighborhood bike shop. If you are a United Mileage Plus member or have a United Chase credit card your first bag is free and the second one will either be free or $40 depending on what type of card you have.
https://www.united.com/en/us/fly/travel/baggage/free-bags-for-cardmembers.html
If you are not a member or cardholder then the fee will likely be $40 for the first bag (bike box) and $50 for the second (normal) bag, but use the "bag calculator page" to make sure. NOTE: Bike boxes do not qualify for the small prepay discount that is mentioned on the bag calculator page; pay the fee at check in.
If you are flying on another airline, check with them to see what they charge.
If you are bringing your own bike to Anchorage and want to store the box it was transported in until you fly out, Downtown Bicycle Rental charges $5 per day to store it for the first week; $3 per day thereafter. Also at the bike rental in its spacious common area is a Park Tool Deluxe Double Arm Repair Stand that you can use free of charge to assemble/disassemble your bike.
Variable II. If you do not currently own a bike, or if you dislike the bike you currently own, or you are thinking of buying a second bike of a different type, then Option B might be the best choice.
Option B: Buy a bike in Anchorage, use it while you're here and then fly home with it as luggage. You'll avoid the cost of renting and end up with the bike you've been thinking of buying and using back home anyway. Your trip to Alaska could be the tipping point to buying a new or owning a second bike.
Anhorage has no sales tax and bike prices are competitive. There are many bike shops in Anchorage. Downtown Bicycle Rental sells Fuji, Surly and Breezer so if you are interested in buying one of those brands and want the bike waiting for you in Anchorage prior to starting your trip it can be ordered in advance with a 50 percent deposit.
Variable III: You are on a tight budget and do not want to bring a bike home after your trip.
Option C: Buy a used bike in Anchorage use it while you are here, then sell it before you leave. Check Anchoragecraigslistbikes or Facebookmarketplaceanchoragebikes. You could also buy a department store bike (Walmart) for about $200 and although it won't perform, last, or re-sell for as much as name-brand bike, it's a cheap way to have wheels over the weeks or months you're here. It is unlikely a cheap bike used for many weeks will be worth the trouble to box up and take home and it will sell for a lot less than what you paid for it so another option is to donate it to charity. AWAKE (Abused Women Aid in Crisis) is always in need of bikes for women and their kids who have left their house in a hurry but still need wheels to get around.