Each Class starts with only the first of its three class abilities. As the first level ability resolves, the Class becomes level 2 and gains the second class ability. As the second level ability resolves, the Class becomes level 3 and gains the third class ability.

If either target of the Level 2 class ability is an illegal target as the ability resolves, the ability won't do anything. If both targets are illegal, the ability won't resolve. If the Equipment is already attached to the target creature, nothing happens.

Each Class has five abilities. The three in the major sections of its text box are class abilities. Class abilities can be static, activated, or triggered abilities. The other two are level abilities, one activated ability to advance the Class to level 2 and another to advance the Class to level 3.

Gaining a level won't remove abilities that a Class had at a previous level.

A creature you control is equipped if there's an Equipment attached to it. You don't have to control that Equipment.

You can't activate the first level ability of a Class unless that Class is level 1. Similarly, you can't activate the second level ability of a Class unless that Class is level 2.

Gaining a level is a normal activated ability. It uses the stack and can be responded to.

There's no restriction on how many Class permanents you can control, whether they're the same or different classes. Each Class permanent tracks its own level separately.