You bring up a lot of factors, but i'll do my best to cover them all. Earth would be able to adapt to having 2 moons with little major difference to the fauna, but nocturnalism would be a less effective adaptation because the nights would be brighter. Look at the last paragraph for more on that.
The Tides would change, if both moons were next to each other, the tide would be higher with their combined force, so living on the coastline would be nearly impossible. If the moons orbits are off of each other, there could be more than 2 tides a day, but the tides would be less severe as the ocean would be pulled in 2 directions instead of 3. Either way, multiple moons makes sailing and coastal dwelling nearly impossible, so travel overseas would have to be in the air or not at all.
Often in mythology, 2 celestial bodies like this could either be expressed as immortalized lovers, or as enemies doomed to chase each other across the sky for all eternity.
The moons appearance can vary greatly, one moon could be smaller than the other, or orbit faster, and that would change how it would look. It is unlikely they would line up, because 2 moons that close together might cause their gravities to pull them together and that wouldn't be good. Solar eclipses would still happen, but the light of the other moon would mitigate most of the shadow effect, so it would only be what we know as a solar eclipse if the second moon was on the other side of the planet, so it would be an even more rare occurrence. The Lunar cycles are caused by the moon's position in relation to the sun, and would be consistent even with more moons because they wouldn't effect each other enough to matter. The moons would not be on the same cycle, as that would mean they were close together and that would cause problems. Lunar calendars would have to be based off a system of partial-month in order to accommodate the different moons.
The more moons you add, the higher chance there is of a potentially world-ending collision, so don't add too many. The more moons on one side of the planet, the higher and more unpredictable the tides, and the less land area your people have to live on. More moons also affects Earth's tilt on its axis and rotation with the different pulls of conflicting gravities. The one moon Earth has is already slowing Earth's rotation, so it is logical to assume seasons would be different and days might be longer or shorter depending on the various moons placements. The tides would also likely change with the seasons.
Any moons you add would have to be significantly smaller than our current moon, or you will need to shrink the size of the current moon to accommodate, or they will likely eject or collide.
That was a lot of questions in one. Next time, try to split it up or narrow down your inquiry. (Though not gonna lie I had a lot of fun answering this) Here are my sources if you want them. 2 moon Earth. 3 moon Earth.