Network fees
Every chain charges its own gas. We do not add to it. The amount you see in You receive already accounts for the network fee on the receive side.
Minimum and maximum
The maximum is the same for everyone: 50,000 USD worth per swap. The minimum depends on the send coin (usually around 10 USD worth, sometimes a touch more for pricier chains). Both numbers show in the widget the second you pick a pair.
What if the rate moves?
On floating, you receive the rate at the moment of execution. On fixed, you receive exactly what was quoted, provided your deposit arrives within the lock window.