I gave a try about playing online games today. I do have hard time, trying to stick to time limits. Which is more beneficial for my development? 1) Sticking to time limits no matter what, even considering the possibility of making a game losing move..? 2) Always trying to read and trying to play correct moves, even if daring to lose by timeout..?
Fortunately for me, I did not face that problem when I was starting to play go. I played FTF, and my games lasted about one hour. I was a deliberate player, and maybe I would have done better to play quickly. Bruce Wilcox recommended finishing a game in 15 minutes.
And there is a value to playing a game where you play a move in one to two seconds, at least occasionally.
I used to go to a club where the players typically took two to two and a half hours to play a game, which I felt was way too slow. A visiting 5 dan once quipped, "Why do they take so long, when they have nothing to think about?"
Now, it sounds like you are also a fairly deliberate player, so I think that the question is pertinent for you. What do you have to think about? Well, you came up with Black 237, which is quite a good move. My guess is that it took you some time to do so. If so, then a slow pace is probably good for you. Don't argue with success.
OTOH, if it only took you a few seconds to come up with it, then you can play well at that pace. Save your deep deliberation for the review.
And don't forget that you can set your own time limits for online games.
A related question is that of getting into bad habits. Spending a lot of time reading out sequences with bad plays unfortunately gets you into the habit of thinking about bad plays. OTOH, making bad plays thoughtlessly is a bad habit, too.
There is one bad habit that you may be falling into, that of wishful reading. Black 257 and 193 were blunders. You assumed that White would connect in response to your atari. That was wishful reading. As it happened, White did connect, instead of punishing your mistakes. That was lucky for you in terms of winning the game, unlucky in terms of learning go. One way to avoid falling into that bad habit is to consider three replies of the opponent to each of your plays. Not that you have to read everything out, but had you done so, you would probably have seen the correct replies, instead of just the one you wanted to see.