Yes, completely. Creating an account, downloading the client and playing cost nothing. The shop only sells VIP perks and cosmetics — nothing that decides a fight, so you are never at a disadvantage for not paying.
Season 6 Episode 3, the classic version most players remember. Current rates, reset rules and server configuration are published live on the Server Info page, so what you read there is always what the server is actually running.
From the Download page. There is a Windows client with an auto-updating launcher, and a mobile client if you want to play on your phone. Several mirrors are available in case one is slow, and the full system requirements are listed on the same page.
Register on the site with a username, an email address and a password — it takes under a minute and costs nothing. Once the account exists you can log in from the game client straight away; there is no approval step or waiting list.
Yes. There is a mobile client alongside the PC one, and both connect to the same server — it is genuinely cross-platform, not a separate mobile version. Your account, characters, items and progress are the same on both: you can play on PC at home, log in from your phone with the same account, and carry on from where you left off.