In theory, as deflation continues and the mining blocks become more efficient, the cost of the transaction will approach .00000001BTC / 1 Satoshi and stop several times at the point slightly higher than where profitability reaches cost. It is also possible that the transaction rate approaches zero.
The reason why this happens is that the competition will lower the price to the point that only the most efficient miners will be in the business. The price reduction is further amplified by the deflation in Bitcoin. We will find the exact stopping point for the most efficient miners who are willing to obtain the lowest profit margin.
This will also be a floating point because as the volume of transactions increases, so will profitability, which will allow miners to further reduce their rates.
To answer more to some of your questions:
1) Are there more specific estimates or calculations in this regard?
A: None that I can find. My prediction is that the transaction fees will have a multi-tiered approach where the most efficient miners will offer "dual" processing fees, one of which would be 0BTC. Miners would divide their processing power (a percentage based on profitability and a simple maximization problem) and would only include transactions that met the highest payment level.
For example, if you include a rate of 0 Satoshi, you will only get 5% of total processing power. If you include a rate of 1 Satoshi, you will get 10% processing power.
2) Is it possible to foresee, since the "degree of network security" is a rather nebulous incentive for most (occasional) users?
A: The degree of network security will improve if users provide their own processing capacity, but this will not be necessary, since mining will be profitable for the most efficient miners.
3) Will they be bound by the software?
A: The rates will be applied by the miners without including the transaction with a too low rate in the chain of blocks. This will cause a significant delay in the speed of your transaction. In the worst case, where EVERYONE in the network requires a fee, you will have to extract your own blockade so that your transaction is processed.
4) Is it better that these rates are absolute or relative to the amount of a single transfer?
A: A miner can choose to accept a transaction and include it in a block based on any criterion that he considers appropriate. It will be interesting to see how the miners choose to adjust their prices.