Thank you so much for reaching out! It sounds like you’re really immersed in Solitaria, and I’m happy to help clear things up.
The Artist Archetype: You’re right that “The Artist” is an archetype listed around page 38-39 in the rulebook. If you’re having trouble finding the specifics, just keep in mind it might be further along.
Which season you’re on: You choose which season you’re currently on. Currently there’s no rules/instruction to first determine which season you’re in.
How Seasons Work: Yes you are right. The Main Deck of 52 cards is used to track the passage of time and seasons. You’d keep drawing from the current season’s deck until it’s exhausted. Then, reshuffle and continue drawing for that same season until the required reshuffles are complete. For example, the Season of Glow lasts through three reshuffles. You can find this rule under Time Management: Date in page 62.
I hope this helps! If you need more clarification or have any other questions, feel free to reach out.