Kasina meditation?

Yes. In Buddha Dhamma, there is no need to do “conventional kasina meditation” in the sense of yogis who keep looking at a fire, chant “fire, fire, ..” and be absorbed in that arammana.
– Some automatically end up with abhinna powers with the Arahanthood. Of course, that does not happen often. The case of Minister Santati is an exceptional case.

Let us summarize the account on Santati’ per the link you provided. Others may want to read the account in the link provided above.

1. He was a Minister to King Pasenadi and won a battle for the King. After celebrating the victory for seven days, Santati was drunk when the Buddha saw him earlier in the day. Later in the day, one of the dancing girls who entertained him died of exhaustion, and Minister Santati was thoroughly distressed. He went to see the Buddha and the Buddha explained to him in a single verse why he became so distressed. The translation there is not that good, but you can get the idea. 
“The root cause for ANY kind of suffering is attachment to worldly things (upādāna.)”
– I have discussed this in detail recently: “Concepts of Upādāna and Upādānakkhandha”
 
2. Just by hearing that verse, minister Santati attained Arahanthood. Not only that, he had attained abhinna powers as well. That is the key point to think about. This account is very similar to that of Vne. Culapanthaka, who had been unable to even memorize a single verse for many months, but attained Arahanthood complete with abhinna powers in a day!
– Also see the amazing account of Ven. Cūḷapanthaka in #2 of “Are There Procedures for Attaining Magga Phala, Jhāna and Abhiññā?”

3. With his abhinna powers, Minister Santati saw that his life is coming to an end. With Buddha’s consent, he rose to the sky and set himself on fire at the moment of death. In the version that I had heard, the Buddha actually asked him to do that so that others could see that he had attained Arahanthood complete with abhinna powers.

4. The point here is that Minister Santati had not cultivated any jhana. He was a warrior who had just led an army to battle. But apparently, he had fulfilled most of the paramita in his prior lives, and “needed only a little push” to get to the Arahanthood.
– He had cultivated jhana in prior lives as well and that is why he (and Ven. Culapanthaka) automatically attained abhinna powers together with the Arahanthood.

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Jittananto

#1 I think it is time to write a couple of posts on “bhavana.” I will try to do that in the coming weeks.

#2 Yes. Jhana and abhinna powers seem to be connected.
– But that does not mean everyone needs to CULTIVATE jhana. How did Minister Santati or Ven. Culapanthaka attain abhinna powers? Did they cultivate jhanas?
– Of course, one could cultivate ANARIYA jhana to higher levels (above the fourth jhana) and attain abhinna powers. Devadatta did. But he lost all that and was reborn in a niraya!

#3. We do know that Angulimala killed almost a thousand people. Did he not attain Arahanthood?
– Unless one has done an anantara papa kamma (killing a parent,an Arahant, etc), even Arahanthood is not ruled out.
– “Account of Angulimāla – Many Insights to Buddha Dhamma”

#4 Yes.

#5 The term “cetovimutti” implies vimutti, which normally refers to Nibbana.
– I don’t think the word cetovimutti can be used to describe any person who has attained even the highest jhana and abhinna powers. Obviously, Devadatta had not attained cetovimutti. He had cultivated anariya jhana and also had abhinna powers at one time. He ended up in a niraya.
– Those who attain Ariya jhana and cultivate them all the way to the highest gets to Arahanthood; they are Cetovimutta Arahants. But there are pannavimutta Arahants who had not cultivated jhana and attain Nibbana. Then there are Arahants like Ven. Sariputta, Ven. Culapanthaka, Minister Santati who are both cetovimutta and pannavimutta Arahants.