Can the bitcoin scalability problem be solved in the long run by increasing the block size limit (either dynamically or statically)?
No. The fees are the incentive for the miners to continue their work, verifying transactions and including them in blocks. Mining is expensive. Eventually, the block reward will reduce to zero and the fees will be the only payment that the miners will receive.
Whatever may change with Bitcoin in the future, the fees must be able to float to the market and that must be protected, although, I do disagree that the current auction model for limited bandwidth is the optimum model for Bitcoin to be using as it is nowhere near scalable.
No. Bitcoin as it is used to day is not capable of replacing traditional use of paper-based or even electronic cash systems.
Increasing the block size would lead to a faster confirmation rate over all, but the requirements of storage space are just not practical enough for really large amounts of payments.
This would buy some time, but not solve the underlying problem of bandwidth and storage space.
No. Miners have operational costs including the computational work required to produce block hashes, internet bandwidth, storage space for maintaining a local copy of the whole blockchain and rent. Transaction fees will have to cover these costs.
Further to this, larger blocks do not solve the scalability problem faced by Bitcoin and other blockchains. This is because larger blocks place greater resource requirements on full nodes (i.e. increased internet bandwidth usage, increased storage space for maintaining a local copy of the whole blockchain and increased CPU usage for validating more and larger transactions).
Higher resource requirements entail higher running costs. The higher the cost of running full nodes, the less people shall run them (some potentially won't even have access to the resources required to run a node with larger blocks).
Ultimately, larger blocks will lead to increased centralization of the network as less and less people run full nodes. This makes Bitcoin less secure and more vulnerable to attacks.