USA Credit Card Accepted?

Cannot specifically address each of your question - BUT -- for our experience - the Scandinavia countries are the most cash-free of all of Europe. We had problems with our mag strip cards not being accepted in automated machines - tickets, etc. If an attendant was available the cards were accepted. Our US cards are chip and signature so I would try to find a true chip and pin. Also I would establish a pin for your cards. I have no experience in Norway but have found that sometimes the pin number will work for a chip and signature card.

It may be hit or miss depending on the machines, your bank's protocol's and the amounts of each transaction. Your bank might be able to issue a PIN for the card, which would normally be for cash advances from ATMs. But that might allow it to work in automated machines. Some machines will detect the card is from the US and doesn't require a PIN and approve the transaction. And your bank may allow for automatic approvals for purchases under a certain amount. Sometimes you may just need to enter any 4 digit number to make it work.

Sorry that isn't a more clear answer, but without a chip card that includes a transaction PIN, there is no easy or consistent answer. You might want to consider getting a card with a chip and PIN for this trip for ease of mind.

I have avoided renting cars in Norway (and in Europe). That said, Norway is one of those Scandinavian cashless countries and credit cards are widely accepted. If you have a US chip and signature card, you may need to find a staffed payment station at the gas stations.

With respect to automated tolls: http://www.autopass.no/visitors-payment

The automated toll stations are all equipped with a camera that reads
the vehicle number plates and toll tags. Foreign registered vehicles,
without a toll tag, will be invoiced by Euro Parking Collection plc
(EPC).

Check with the rental car company as to how they will charge you for tolls. If you rent an Norwegian car, the Norwegian rental agency will be charged toll and I suspect that the the toll will be passed on to you. There may be an administrative fee added to the tolls.

My experience around the Alesund area, Bergen, and Oslo, is that American credit cards are accepted some places and not others. We used our cards to pay for gas at automated pumps - sometimes we had to try more than one card but always had one that ultimately worked. There are plenty of manned stations though if you don't want to deal with that.
They were accepted by the hand-held ticket machines used by the attendants on car ferries.
Grocery stores were difficult - we tried to use one the first time and many employees had to be consulted before they figured out how to charge us and have us sign the receipt. I think we might have gotten free groceries that day!
We did go through a toll tunnel north of Alesund (are you talking about the one near Krisiansund?) and we just paid cash - there is a manned booth. There are many other tunnels around Alesund but that is the only one I remember having to pay a toll. I'm sure your rental car will come with the toll sticker that you have to have when driving in Norway.
If you are in doubt just carry plenty of cash with you. We were always able to use our cards at restaurants and shops.

Thanks very much to all of you who answered my query! I will call the credit card company and
try to get a pin. (I've tried before, but maybe persistence will pay off.) If that doesn't work, you
have given me enough information that I think I can avoid being stranded. I'm particularly encouraged
to find out that the tunnel booth and some gas stations offer human contact rather than just a
machine. Maybe cash is still a good reserve for those of us who are technologically challenged!

I have never had a train-ticket or bus-ticket vending machine refuse my US credit card, but I always have enough euros on me to use cash in case the machine offers that option and I need to use it. That's probably why my card always works!