Does sebastian likes the servants ? or at leaat cares for them ?
i think the concept of liking someone in the human sense is foreign to sebastian, but he absolutely respects people. for a demon, he's surprisingly fascinated by humans.
yana once said that sebastian views humans as grasshoppers, but that was back in 2009 during the circus arc. while he did approach people very coldly at the time, he still showed them respect whenever they could serve as teachers to him in some regard. in agni's case, it was his absolute devotion to his master; in tanaka's, being the perfect butler; and in nina's, her sewing skills.
which is actually pretty funny considering how often he argues with her about the clothes she picks for ciel, yet at the same time he never belittles her abilities and knows perfectly well that he can't compete with them. sebastian is a narcissist and loves being praised, and excessive modesty certainly isn't one of his flaws. however, when he made a dress for sieglinde, he admitted that it didn't look as good as something professionally made, and when he and ciel went to the hotel to conduct their investigation, he preferred owing nina a favor so that ciel could have the best clothes possible rather than trying to make them himself.
the respect he showed agni came through in the fact that he viewed his devotion not as something pathetic, but as something admirable. meanwhile, tanaka remained a role model for him. not only does he remember his words, he also follows his judgment. when he wanted to touch ciel after he woke up from the gas poisoning, tanaka stopped him, and sebastian listened, operating under the assumption that tanaka knew better.
i know i'm going off on a tangent a bit, but i'm trying to establish where my observations are coming from.
so yes, he respects other people for their skills if there's something he can learn from them. and let's not forget that it was sebastian who chose mei-rin and bard. he's repeatedly shown pride in the servants' combat abilities. mei-rin can shoot from a distance greater than sebastian's hearing could register. he called finny a skilled assassin. bard's primary role was keeping them all in line. snake proved useful time and time again. as irritating as they can be to him, they're still valuable servants in his eyes.
and while at the beginning he may genuinely have seen them as grasshoppers assigned to perform a task, i think his perspective changed. just as he cares more about ciel now, he also cares more about the servants.
as usual, the biggest turning point was the attack and his injury aboard the campania. i see a parallel here with his words about bard: "you fear death, as humans should. you must be the only one in this manor who does." sebastian's transformation is precisely caused by the fact that he himself could have died, which was a turning point when it comes to him becoming more human.
not only does he trust them enough to entrust ciel's life to them, he also knows perfectly well that he can rely on them, as shown by things like their rescue during the prison transport.
i also don't think he would handle the book of murder situation the same way now. he wouldn't fake his death anymore, because he understands their feelings and attachment to him much better.
so, returning to the question: does he like them?
i don't think he understands the concept of liking someone.
but over time, he absolutely learned to care about them.
the best example is probably his conversation with ciel in chapter 212, when they're discussing who can handle themselves and who they should be worried about.