I would be really grateful if someone would explain how fee and transaction time are calculated.
You can't calculate the transaction time. That's because the fee estimate is based on past transactions, and the actual confirmation time will depend on future transactions and future block times.
So the best you can do is an estimate, and if things change (for instance when it takes longer to find the next block), your estimate was wrong.
Don't forget that the recommended fee is usually based on a fast transaction, which often isn't necessary. If all wallets do that, all you accomplish is ever increasing fees when blocks are full. Based on Johoe's current overview, I expect 15 sat/byte to confirm quite fast. 10 sat/byte might take a few hours. But if the next block takes an hour, 40 sat/byte might not be enough to get in there.
If I send bitcoin at 08:00, and wish to receive it on other address at 08:00 next day, which amount of Satoshi per byte should I use?
It doesn't work that way. You can use
Locktime to create a transaction that can't be confirmed before a certain time/date/block, but that means you'll have to broadcast it the next day.
I can't think of a single use for what you're asking though, usually it's not a problem if someone gets paid a few hours before expecting payment.