You can look at the top card of your library whenever you want (with one restriction; see below), even if you don't have priority. This action doesn't use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand.

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.

If the top card of your library changes while you're casting a spell, playing a land, or activating an ability, you can't look at the new top card until you finish doing so. This means that if you cast a spell from the top of your library, you can't look at the next one until you're done paying for that spell.

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.

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

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.

The cost reduction applies only to generic mana in the total cost of spells you cast from anywhere other than your hand.

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.

You must pay all costs and follow all timing rules for lands played and spells cast from the top of your library this way.

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

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as a flashback cost), add any cost increases (such as kicker costs), then apply any cost reductions (such as that of this ability). The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.