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

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.

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.

The cost reduction applies only to generic mana in the total cost of noncreature spells you cast.

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.

The additional 2 damage is dealt by the same source as the original source of damage. The damage isn't dealt by Artist's Talent unless Artist's Talent is somehow the original source of that damage.

If another effect modifies how much damage a source would deal, including preventing some of it, the player being dealt damage or the controller of the permanent being dealt damage chooses an order in which to apply those effects. If all of the damage is prevented, the effect of Artist's Talent's last ability no longer applies.

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.

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.

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