So most rock nowadays isn’t man made in the sense that we think.
It’s can be any of the following:
Dry rock quarried from long extinct reefs (commonly called Marco Rock)
or
Manufactured rock (Caribsea Life Rock or other branded rock) - this “man made” rock usually made out of a cement, shell, sand and other materials and then usually dyed purple to look coraline covered
Then there is aquacultured live rock which is essentially taking the Marco rock (or similar such as Walt Smith Rock (man made), and placing it in the ocean for a few to several years and then selling it as live rock. This is rarely called man made rock as by the time we use it, it’s long been made “real” even though man placed it in the ocean.
You then have truly man made rock which hobbyist make similar to the manufactured rock but just done by a hobbyist and usually denser/more solid.
Finally, you have real live rock, which is ocean collected rock right from the reef
Your “standard cycle” will vary depending on your tank. Some bottled bacteria can essentially “instant cycle” a tank to where you can start slowly adding stuff within a few days.
Then you have people who do an ammonia cycle (add ammonia and let the tank process from there, I’m not familiar with this method).
If you use aquacultured or real live rock, you just need to watch your initial ammonia spike from any die off. Once you start having a 0 (or as close to 0 as possible) reading on ammonia and then nitrite you should be cycled (this can be a few days to a few weeks
Quantity of rock is your own option. Some do as few as just under a pound per gallon to 2 or more pounds per gallon. This can be an issue to calculate as some rock is heavier for the same size pieces. So it’s more what you think looks good in your tank.
I hope this helps!