A fork will occur when on the initial chain, there is split to two or three different chains. Miners and mining pools have to choose what chain they will continue to mine with and obey those consensus on that chain.

Usually mining pools, nodes, and miners will choose a longest chain to continue their work (mining blocks and confirm transactions). They will less likely to choose shorter chains as it contains more risk for them. The second scenario only happens when some mining pools intentionally support a consensus which leads to that shorter chain so they clearly know what they are doing when they choosing that short chain, then become a fork.

Hell no, do you know that most of forks are useless and will die with time?

A comparative analysis of Bitcoin forks.
How many Bitcoin forks are there?