The Battle Pass can be bought from MY.GAMES Market. It's also available in-game (press 'F5' to access the seasonal interface) and Steam.
Yes, the Free Pass has many Tiers of rewards that you can earn as you play for free!
There is more content to unlock in the Battle Pass, including season-exclusive Attire. Otherwise, both function in the same way when it comes to progression and unlocking rewards.
Complete Seasonal Challenges and matchmaking battles to earn Glory. The more Glory you accumulate, the more you'll level up your Battle Pass, and the more rewards you'll earn! Special bundles will be available later in the season that allow you to boost the level of your Battle Pass.
No matter when you purchase the Battle Pass during this season, you'll receive all the premium rewards from the Battle Pass up to your current Tier. For instance, if you reach Tier 80 on the Free Pass and then buy the Battle Pass, you'll receive all premium rewards up to Tier 80.
Yes, any in-game content unlocked from the Battle Pass is yours to keep forever. However, if you don't unlock certain rewards before the season ends, they're gone forever!