In Mistborn, there are the 3 types of powers: hemalurgy, allomancy, and feruchemy.
Can Kandra use hemalurgy to take Allomancy and Feruchemy from humans, and then use it themselves?
Yes, in both cases.
We have known for a while that they can be given Allomantic powers by giving them the appropriate Blessing. No one on Scadriel knows how do to it, except Harmony.src In addition, a Kandra can burn Lerasium the same was a human would, and gain Allomancy that way.src
We just recently (with the release of Shadows of Self) learned that Kandra can also steal Feruchemy from others via Hemalurgy. In this case.
the Blessing involved isn't even know to Harmony, which implies that another shard holder is interfering on Scadriel.
For their part, the Kandra don't seem to be aware that Harmony knows a Blessing that would give them Allomancy. While discussing this exact topic, one of them says:
Maybe that's why she could use stolen Allomancy [...] when other kandra cannot.
Since all Kandra can speak directly to Harmony via their Blessings, this implies that Harmony is keeping that information from them.
answered Oct 8 '15 at 14:06
As Mike has said, they can be granted Allomantic powers via the appropriate Blessing, or by burning Lerasium.
Revealed in the new book...
is the fact that Kandra can take and use Feruchemy and Allomancy from other people using Hemalurgy. The main antagonist "Bleeder" in the book is a Kandra that does exactly that. The details of how to do it are in Marsh's book, given to Marasi at the end of Alloy of Law.
Quotes from Shadows of Self:
And what are any of you going to do about someone who can move at the speed of a thunderclap?
And
The mists churned. Wax stumbled back, swinging his gun toward something that had passed in a blur, leaving a corridor of swirling mist. Bleeder. Moving with Feruchemical speed.
I will point out that
Bleeder may be the only Kandra to do this, given that it is using a spike of an unknown metal (unknown to Harmony!) from an unknown source (Probably another shard holder, Trell is given as a possibility) to transfer Feruchemical powers.
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Are we sure that letting Kandra use Hemalurgy might not have been some power of, say, Autonomy? – Adamant Oct 9 '15 at 0:05
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Technically, the Kandra are always using Hemalurgy (at least one spike to be sentient). The question is regarding the type of powers that can be transferred. – AerusDar Oct 9 '15 at 0:12
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Sure, good point. What I meant was, is it perhaps Autonomy who is allowing Bleeder to Hemalurgically acquire Allomantic or Feruchemical powers? I very much doubt this is the case, but it would be nice to have some solid evidence against it. – Adamant Oct 9 '15 at 0:15
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It would be very interesting if it were so, given that Bavadin is on a different planet. – AerusDar Oct 9 '15 at 0:50
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Are we sure about that? I feel like Bleeder's actions definitely bespeak someone influenced by Autonomy. Autonomy also seems most likely, of the Shards we know, to interfere on Scadrial, given Harmony's fairly active management of his people. Odium of course is another option, but I don't think it would go one-on-two. In fact, I suspect it never did: Odium and Autonomy would have had good reason to dislike Devotion and Dominion. – Adamant Oct 9 '15 at 1:44
