What was the point of the first scene with Wallace and Luv?

Luv has one simple motive: she wants to be the best (she reveals this when she seemingly killed K). And Wallace constantly reminds her of that, especially in the scene where he kills the newborn. His message in that scene is that Luv is the only one he can trust to bring the child. As such, the tear she shed might have been a tear of joy. She is in no way a sympathetic character forced to comply, and I will expand on this later.

For the time being, let's go through the 4 scenes you've listed:

1. She kills Rachel "seemingly without regret" because she thinks she is the best replicant, and is not hesitant in the slightest sense to kill another replicant. Remember, if she can be jealous of K, then she can also be jealous of any other replicant that might outperform her.
2. She plans to lie to Wallace because, once again, she wants to prove her father that she is the best. She is afraid of disappointing him.
3. She is extremely jealous of K. He is pretty much her rival, not because he is against Wallace, but because he might be better than her. So she is willing to cause him as much pain as possible.
4. She really has to find the child and bring it to Wallace. She uses K to find the girl for her. This is presumably when she started getting jealous of K's abilities.

Now, is she really a cold, ruthless operative? I don't think so. The movie portrayed her as generally childish. Just like a child, she wants to be the best, and wants to impress her parent. In the scene where she's torturing Joshi, you can hear a certain tune in the way she delivers her lines. She almost sounds playful, as she gains an upper hand, squeezing Joshi's hand into the glass.

She is mentally only 5 years old as well, as her implanted memories don't really mean anything to her (she knows they are fake).

If you're wondering why K doesn't act like a child:

1. He never had a motive, let alone a childish motive. While Luv had somebody to impress, K did not. He was hated by both replicants (because he killed them), and humans alike.
2. After he figures out he is the child (before the plot twist), his memories suddenly became real to him, and they now have meaning. So he is emotionally much more mature.

Much as madam was fighting for something she strongly believed in (the continuance of the status quo and preservation of the maximum amount of life) and was willing to go to great lengths to achieve/protect it, Luv truly believed in Wallace's goal of spreading human/replicant life throughout the stars, and ultimately preserving life, regardless of the short term cost. Though she still had empathy, her conviction outweighed and largely allowed her to suppress it, even in the face of committing horrendous acts of violence - this self employed imbalance led her to develop a strong sense self loathing, which only fed her fury. Wallace demands devotion and violence, and Luv is honored to serve him, in spite of herself. She is pained by her own actions, just as Wallace intended her to be. He's one sick bastard, and she's the epitome of a zealous acolyte.

I believe Luv's actions are oriented towards her own survival, and that reflects Wallace's words during this scene, according to which the key to replicant technology is understanding the will to live demonstrated by living beings.

During that scene Wallace destroys the last remnants of compassion Luv had, making her understand that he will not tolerate her failure, that he expects her to obey without emotions, that he would kill her as easily as he kills any other replicant. She is scared of being witnessed as crying, and unconsciously resolves to giving up her empathy.

Actually Wallace managed to remove humanity from her heart. Actually he is doing the opposite of what he is aiming at ; he really did not understand what life is.