Since nobody has mentioned it yet that I saw, I'll just say that the term 't50' refers to the predecessor of the arena and no longer exists, having been replaced by the arena several years ago. It was a game mode where you would be randomly set against one of the currently loaded decks of the 50 players with the highest overall score in Elements at the time. It was generally too easy because many of the top 50 players would intentionally leave up 'farm' decks when not actually playing the game, i.e. decks full of rares for people to get in the spins but no way for the AI to actually win a game. It was replaced by the arena, which is a much better designed system overall.
For saving decks, if you use the import/export function, you can copy/paste the code in there (in the previous post, the thing that stats with 5c6 and ends with 8pn. Each 3 digit thing corresponds to one card in the deck. There is no in-game way to save decks, beyond that the one you have currently loaded will still be loaded when you play again. I keep a notepad file on my desktop with decks and I also have a bunch on threads in the forum that I have shared for other people's reference as well.
As for decks to play against ai3, I haven't been there for a very long time, but when I started Elements (having a minor heart attack, as I think it was about 5 years ago now...) I started with the life deck, and I quickly built a deck with 6 frog 6 cockatrice 6 adrenaline 1 druid staff and 11 pillars, and started upgrading that as able. I don't know how effective that deck still is, but it was dirt cheap to make, at least in the unupgraded version. (the druid staff is a rare; I took it when I finished my weapon quest. If you don't have one, don't worry about it; a short sword will take its place fine. You could also just use another pillar or experiment with something else like a dragon or mitosis) I would guess, however, that most of the ai3 decks would lose to something like 6 dimensional shield 4 psion 4 fractal + quanta or 6 dimensional shield 6 phase dragon 3-5 more aether cards + quanta.