If Buddha had unconditional love, why did he "kill" some of his monks? I recall there is a sutta where the Buddha said he "kills" some monks, that is, completely ignores them or something similar. 

Is this contrary to metta (unconditonal love)?
The "killing" reference would be this one probably -- Kesi Sutta (AN 4.111)

Perhaps that's analogous to a doctor's not giving medicine to a patient who won't benefit from it.

And perhaps the Buddha had the welfare of others -- the whole Sangha -- to consider too.

Another instance is Channa in DN 16.

And there are a few other examples on pages 89-90 of Piya Tan's analysis of the Kesi Sutta:


  The untamable
  
  Those who cannot be tamed. While most of the suttas record how the Buddha’s
  teachings convert many and inspire others, there is a handful of important discourses where,
  apparently, the protagonists lack the capacity for spiritual change. Interestingly, in all such cases, the
  Buddha does indeed teach them the Dharma. However, for some reason, the protagonists remain
  unmoved despite being admonished by the Buddha himself.
  
  Such discourses are very few, that is, where the protagonists (one may even call them “antagonists”) are “dead” to the Dharma-Vinaya.
  The best known of these are:
  
  
  the Mahā Taṇhā,saṅkhaya Sutta (M 38), where the monk Sāti holds on to the wrong view that our
  consciousness passes on unchanged in rebirth;34
  the Alagaddûpama Sutta (M 22), where the monk Ariṭṭha wrongly views that sensual pleasures
  (including sex) are not “stumbling blocks” to the celibate holy life;35
  the Udumbarikā Sīha,nāda Sutta (D 25), where, despite listening and accepting a long inspiring
  discourse from the Buddha, the wanderer Nigrodha and his followers still neither renounce nor go for
  refuge.
  
  
  The most notorious case of one who is “dead” to the Dharma-Vinaya is clearly the monk
  Deva,datta. Despite being the Buddha’s cousin and listening to numerous Dharma teachings, he still
  shows antagonism against the Buddha, desiring to take over the leadership of the monastic sangha from
  the aging Buddha. The Devadatta narrative where he is depicted as the Buddha’s antagonist is, however,
  not without problems, and should be carefully studied to understand its significance.
  
  The most famous case of a person who seems to be intractable is the elder Channa, the erstwhile charioteer of the Bodhisattva himself.38 On account of Channa’s closeness to the Bodhisattva and
  then the Buddha, he became arrogant, thinking “Our Buddha, our Dharma,” besides his inherited conceit
  of being a kshatriya (khattiya,māna). Channa’s “butler” narcissism and arrogance were, in the end, selfdefeating. He failed in his tasks as a monk even while the Buddha lived. While dwelling in Kosambī, he was
  unwilling to acknowledge an offence he committed that the Buddha decreed a formal act of suspension
  (ukkhepaniya,kamma), forbidding him commensality (eating together) and dwelling with the monks.
  
  He continued to commit other offences, especially disrespecting and reviling senior monks. One of
  the Buddha’s last acts was to instruct Ānanda to impose the “supreme penalty” (brahma,daṇḍa), that is, a
  total boycott of Channa by the sangha.41 After the Buddha’s death, Ānanda executed the order.
  
  The closing of Culla,vagga 11 of the Vinaya records how when Ānanda conveys the supreme penalty to
  Channa at Ghosit’ārāma, in Kosamb, he faints at the thought of being boycotted by the order. Almost
  immediately Channa diligently works to correct himself—as movingly reported in the (Lakkhaṇa) Channa
  Sutta (S 22.90; V 2:292).
  
  The (Lakkhaṇa) Channa Sutta (S 22.90) records in an almost humorous tone, how he
  attempts to seek Dharma instruction from other monks. Apparently, no monk actually boycotts him,
  since they try to answer his questions, albeit careful to not offend him. Finally, Ānanda teaches him the
  Kaccāna,gotta Sutta (S 12.15) on how dependent arising counters the two extreme views of eternalism
  and annihilationism, and how self-view is replaced by the realization that it is only dukkha that arises and
  ceases—and he breaks through to the Dharma. The supreme penalty is automatically lifted at the
  moment of Channa’s final attainment.
  
  This is perhaps the only account we have of any monastic close to the Buddha who is apparently
  declared “dead” to the sangha. However, by his own efforts, Channa returns alive and well to be with the
  sangha, in due course, as an arhat.


The Kesi sutta is about tameable and untameable. I think you've quoted "little dust in their eyes" yourself. Maybe it's not appropriate to question how the Buddha handles the supposedly "untameable".



Whether the Buddha behaves morally and maintains a mind of good-will is presumably unconditional, unaffected by the behaviour or temporary misbehaviour of others.

You might read Positive Response -- How to Meet Evil With Good for example if you can.

It suggests that "tit for tat" is a common strategy in the world but, it says, never works in the realm of spirituality. It references the (famous) Parable of the Saw, for example.

One other thing I'd note about the Buddha is his ability to enter the minds of others and to know when they are ready or not ready -- I think you see that in suttas like AN 8.30.

It might be a mistake for you to imagine that you can do the same -- to enter the minds of others.

It might also be a mistake to assume that they can behave unconditionally -- and unaffected by real or imaginary misbehaviour of yours, by their own projections, etc.

But by definition it means to try to behave well and with good will even if someone else doesn't.