This is such a good scene. Every time I watch it I find something new to love, and other ways to interpret it.
1. Why does Zhao Yunlan want Shen Wei to officially join SID? What’s wrong with being an on-call unofficial consultant?
This is a great question. It's puzzling, because, as you say, he's already doing the job, just unofficially.
Because this scene bookends the one with Minister Gao, I'd like to believe that Zhao Yunlan is actually trying to protect Shen Wei by giving him an official role at the SID. Since he knows Shen Wei is the Black-Cloaked Envoy, this is a way to specifically protect Shen Wei's Haixing identity. If Professor Shen is a consultant with the SID, then he's much less suspicious if, say, he knocks out a bunch of wedding guests to stop them killing each other.
2. Why doesn’t Shen Wei want to join SID? I can’t really divorce this scene from the rest of ep 14, especially the drive to Haixing Inspectorate.
The poor man already has two jobs.
To answer more seriously, I think you're right to bring up the drive. Shen Wei pretty much says he would stay away were it not for the Hallows, and that's what he did before the events in canon. The SID's mandate is basically anti-Dixingren, so I can't imagine that he's thrilled getting further involved with them. Involvement with Zhao Yunlan is another matter entirely, though.
3. Why is Shen Wei so apprehensive in this scene?
He put so much effort in keeping his identity hidden, even if he wasn't particularly good at it. I believe his reasons were at least partially based in fear--fear of what Zhao Yunlan would think, fear that he'd put him in danger, fear of how he could influence the timeline. Now he's faced with the thing he was trying to avoid happening. He's uncertain, and lost in time and memories. Which does not stop him going, "Who says I can't erase your memories?" to Zhao Yunlan, and I love him for it.
4. Why is it the last appeal that works? Shen Wei won’t join SID for friendship, he won’t join for guilt, he won’t even do it for the sake of Zhao Yunlan’s puppy eyes.
I think it's frustrating for Shen Wei to be confronted with all the jokey entreaties and the playful flirting now, just after one of the barriers between them was broken. Zhao Yunlan knows he's the Black-Cloaked Envoy, but they're not really any closer. From Shen Wei's perspective, I think Zhao Yunlan appears insincere, or at least not as invested as Shen Wei. The request that eventually works is the one that does not call on any existing personal connection between the two of them.
I'd say this is completely due to time-travelling shenanigans. The reasons why Shen Wei was keeping things from Zhao Yunlan haven't gone away with the BCE reveal.
6. How conscious is Zhao Yunlan in his manipulations? Is it just the detective in him? He’s not subtle here: what is Shen Wei thinking, comparing him to Kunlun?
He's very deliberately testing the waters, in my opinion. He's probing to see what aspects of his previous connection with Shen Wei, both as Professor Shen and as the Black-Cloaked Envoy, were real. They're constructing a new dynamic, and this is how Zhao Yunlan is making sense of it. And Shen Wei is making the same adjustments, I think, while also being hit with his memories of Kunlun, so he has to adjust not only to Zhao Yunlan knowing about the BCE, but to him still not being Kunlun. Of course, the difference is not in Zhao Yunlan, but in their level of intimacy. However, like I already mentioned, on some level, it must be disappointing that the reveal did not change more in their relationship.
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1. Why does Zhao Yunlan want Shen Wei to officially join SID? What’s wrong with being an on-call unofficial consultant?
This is a great question. It's puzzling, because, as you say, he's already doing the job, just unofficially.
Because this scene bookends the one with Minister Gao, I'd like to believe that Zhao Yunlan is actually trying to protect Shen Wei by giving him an official role at the SID. Since he knows Shen Wei is the Black-Cloaked Envoy, this is a way to specifically protect Shen Wei's Haixing identity. If Professor Shen is a consultant with the SID, then he's much less suspicious if, say, he knocks out a bunch of wedding guests to stop them killing each other.
2. Why doesn’t Shen Wei want to join SID? I can’t really divorce this scene from the rest of ep 14, especially the drive to Haixing Inspectorate.
The poor man already has two jobs.
To answer more seriously, I think you're right to bring up the drive. Shen Wei pretty much says he would stay away were it not for the Hallows, and that's what he did before the events in canon. The SID's mandate is basically anti-Dixingren, so I can't imagine that he's thrilled getting further involved with them. Involvement with Zhao Yunlan is another matter entirely, though.
3. Why is Shen Wei so apprehensive in this scene?
He put so much effort in keeping his identity hidden, even if he wasn't particularly good at it. I believe his reasons were at least partially based in fear--fear of what Zhao Yunlan would think, fear that he'd put him in danger, fear of how he could influence the timeline. Now he's faced with the thing he was trying to avoid happening. He's uncertain, and lost in time and memories. Which does not stop him going, "Who says I can't erase your memories?" to Zhao Yunlan, and I love him for it.
4. Why is it the last appeal that works? Shen Wei won’t join SID for friendship, he won’t join for guilt, he won’t even do it for the sake of Zhao Yunlan’s puppy eyes.
I think it's frustrating for Shen Wei to be confronted with all the jokey entreaties and the playful flirting now, just after one of the barriers between them was broken. Zhao Yunlan knows he's the Black-Cloaked Envoy, but they're not really any closer. From Shen Wei's perspective, I think Zhao Yunlan appears insincere, or at least not as invested as Shen Wei. The request that eventually works is the one that does not call on any existing personal connection between the two of them.
5. Why can’t Shen Wei tell Zhao Yunlan why he’s helping him?
I'd say this is completely due to time-travelling shenanigans. The reasons why Shen Wei was keeping things from Zhao Yunlan haven't gone away with the BCE reveal.
6. How conscious is Zhao Yunlan in his manipulations? Is it just the detective in him? He’s not subtle here: what is Shen Wei thinking, comparing him to Kunlun?
He's very deliberately testing the waters, in my opinion. He's probing to see what aspects of his previous connection with Shen Wei, both as Professor Shen and as the Black-Cloaked Envoy, were real. They're constructing a new dynamic, and this is how Zhao Yunlan is making sense of it. And Shen Wei is making the same adjustments, I think, while also being hit with his memories of Kunlun, so he has to adjust not only to Zhao Yunlan knowing about the BCE, but to him still not being Kunlun. Of course, the difference is not in Zhao Yunlan, but in their level of intimacy. However, like I already mentioned, on some level, it must be disappointing that the reveal did not change more in their relationship.