1) In 2140 when all of the Bitcoins have been mined, what motivation will miners have to continue mining?
They will mine for the transaction fees. Long before the end of the block subsidy, the transaction fees will become the main source of income for miners.
2) After the Bitcoins run out, will the experiment be over? Will we just all move to a brand new Bitcoin 2.0?
They won't "run out". The existing bitcoins will remain in circulation and will be used for products, services, and transaction fees.
3) Will testnet Bitcoins ever have any value?
Unknown, but unlikely to have any significant value.
4) Do you think modifying Bitcoin so that it indefinitely inflates over time would be a good idea?
No.
I personally believe that Bitcoin should not stop inflating. Miners will have almost NO incentive when mining after the block reward is gone. Mining fees aren't high enough and people will have to pay a premium to get their transactions completed.
You are attempting to predict miners incentive based off of today's transaction volume. If bitcoin doesn't fail in the next few decades, the transaction volume will increase and the income from transaction fees will therefore increase as well. Eventually the revenue from fees will exceed the revenue from the subsidy. There will likely be third-party transaction processors that will exist eventually as well. These payment processors will be able to spread out the blockchain transaction costs across many smaller off-chain transactions.
Even if we doubled block halving to 8 years instead of 4, it would help.
No thanks.
Also, do you think a shorter confirmation time will help Bitcoin out as well? As adoption grows and the economy expands, confirmation time needs to change. An hour long confirmation time simply isn't acceptable for the majority of people.
Confirmations don't typically take an hour. Most people will find that it is sufficient to wait for just one or two confirmations for high-risk transactions. Low rick transactions will be accepted with 0 confirmations. Third-party transaction processors will be able to guarantee payment with 0 confirmations as well.