Please explain to me why I can Ron the opponent's discard? (see screenshot)
I suppose I'm in furiten.
But I don't understand why - I tried to read the rules, it states that I can't win on an oppenent's discard when I have discarded the winning tile before. But I didn't discard a 2-character tile yet? Or are even other tiles involved for the furiten (chi'd on 6-bamboo)?
Well, the good news is that you are not in Furiten. The waits on that hand are 2-char, 5-char, and 8-char, and none of those have been discarded by either player, so Furiten does not apply.
What you DID fall victim to is the yaku requirement. That hand does not meet the requirements on account of it being open. It would need to be a concealed hand for a win by Tsumo OR reached (which requires a concealed hand) for a win by either Tsumo or Ron. Despite this, you would be tenpai should it come to that point because you only need one tile to "complete" your hand (despite the fact that you cannot go out with that hand).
Looking at the hand and the discards at that time, it would appear the best course of action is to hope your opponent discards a green dragon so that you can pon it (or hope you draw one yourself) and convert your 1-dot triple into eyes. Yakuhai (Triple of any dragon, seat wind, or round wind) is applicable even if the hand is open, so it would make the hand legal to win by Ron on a 2, 5, or 8-char (assuming I remember Furiten rules correctly).
Note that if you were to draw (or meld in) a 2, 5, or 8-char before completing this switch and discard a 1-dot, I'm fairly certain you would be in Furiten from that point because your waits would be a Green Dragon (which makes a hand you can go out on) and a 1-dot (which makes a hand you cannot go out on), and you would be required to win by Tsumo.
As goldPseudo also pointed out, the following related question is also pertinent to open hands in general:
It doesn't look like you're in furiten. However, in riichi mahjong, a hand also needs at least one complete yaku (multiplier) before it can be completed, and I'm not seeing one in your hand.
If your hand were still closed, you could easily supply the needed multiplier simply by calling riichi. However, calling riichi requires a closed hand, and since you'd already called the 678-bamboo meld your hand is already open.
Otherwise, your best option would probably be to make a set of three green dragons (which would provide the "yakuhai" yaku, even on an open hand) and toss one of the 1-bamboo.
See also the answers to this related question:
