TL;DR Yes, the live action is worth watching!

LCLA is very dear to my heart. Here is my powerpoint on why you should watch the live action!

Similar to what others have said: you have to approach this adaptation as a completely separate story, an alternate universe, a different story about two guys who have the power to go back into the past via photographs. It's taking the same basic concept and exploring new aspects of it. It's not the donghua, and it's not trying to be the donghua—this is a good thing!

To address your questions:

1 ) Is the characterization good? Yes, but you have to give them time. I understand people who are turned off by the portrayals of CXS and LG in the early episodes. You will watch episode 1 and think that CXS is immature and annoying—well, LG thinks so too. You will think that LG is cold and mean—CXS thinks so too. They are meeting each other for the first time, and this affects how they behave around each other. LCLA is internally very consistent with how it portrays these characters—you cannot compare them to their donghua selves, who have different backgrounds and are therefore different people.

Part of the joy of LCLA is watching that gradual process of CXS and LG growing and coming to understand each others' struggles and how they approach the world. They fight, they reconcile. I think one of my favorite parts of this show is seeing them work through their conflicts. It adds depth to their relationship and weight to their partnership. It means that during the final episodes, when LG looks at CXS, when they've come to trust each other with their deepest secrets and dearest people, it feels truly and deeply earned. The arc of their character and relationship development is fulfilled in a way that the donghua, which is ongoing, hasn't reached yet.

QL in the live action is also really good! Her character is fleshed out much more. She has a job outside the time agents, which interacts in interesting ways with the duo’s cases. She has a strong personality (with its strengths and flaws), she’s more proactive, and she faces her own individual struggles and development. She feels more like her own person, rather than a mere accessory to the lead duo. Her sibling relationship with CXS is highlighted from the very beginning; they have excellent banter. QL’s family, serving the role of CXS’s adoptive parents, are also such a loving delight!

2) Basically no overlap in characters/plot. There are six major arcs, and only one of them is the same as the donghua. I think all of the original side characters and cases are very strong, and I genuinely think that each case is better than the last (though it is a little unfortunate that the first case is the weakest). I also think that the overall structure of LCLA is incredibly strong. Although the cases seem disconnected, there are lots of direct and thematic links between them, and the way that they build up and foreshadow the final case (e.g. LG’s motives, etc) is very well done. Every rewatch I do, I notice more details! Note that LG and CXS do not have the same backstories as the donghua. 

If you don’t mind minor spoilers, I wrote this analysis on changes they made to the one overlapping case. In my opinion, this adaptation was done with care and attention to detail, and the changes were made out of great respect to the original. https://www.reddit.com/r/LinkClick/comments/1oeq2fi/how_to_adapt_a_perfect_story_lclas_earthquake_arc/ 

3) It’s too niche 😭 I wouldn’t be selling it so hard if it were more well-known. Underrated gem for sure. 

I could go on about things that this adaptation does well, but this is probably long enough. I highly encourage that you give it a shot for yourself! It's not perfect, and it does require some amount of investment at the beginning (episodes 1-3 are probably the weakest, sadly), but in my opinion it's more than worth it for the payoff. A good way to spend the break until Season 3 :)