What is the nature of a true cognition in Buddhism, or what Buddhism considers as truth?
Upper-case Truth would be Being. As Aristotle notes, the only certain form of knowledge is 'knowledge by identity'. We can know what we are. All else is speculation.
Is it the same as what people consider a logical conclusion made with an empirical process?
Definitely not. You might have made a calculation error or misperceived the empirical facts.
I feel it cannot be exactly that as various truths exist in Buddhism that aren't easily verifiable with mere deduction.
No absolute truths are verifiable by deduction. This would be the reason why any purely scholastic metaphysics is hopeless, as history shows.
In addition, how important is truthful cognition/perception in Buddhism? How far can you get practicing things like mindfulness, compassion, etc. without being capable of ascertaining things as 'true' for oneself.
Well, we have not made much progress if we have not ascertained to some extent the truth of the teachings. As time goes by truthful cognition would be vital but it would not be possible at the start, prior to understanding something of the nature of Reality and the relationship between cognition and consciousness, so the best course is to not worry about deduction and just sit and wait to find out, much as the Buddha advises. I prefer to do the sums, but this does not bring 'true' knowledge, only good arguments for dealing with sceptics.
The proviso would be that it is possible, as Nagarjuna demonstrates, to demonstrate in logic that a neutral metaphysical theory is the only one consistent with reason. This is lower-case knowledge, but valuable and important nevertheless. It surprises me that more Buddhists do not realise that the teachings solve all formal metaphysical problems.
Finally, and I guess I should've asked this before, what effects/qualities does true information have in Buddhism? Is it timeless? Universal? Beyond doubt?
Yes, timeless, universal and beyond doubt. But only when we know it is. If we do not know then it is not knowledge. Think of it as an immediate knowledge of pain. When we have an immediate knowledge of pain we do not doubt it. Immediate knowledge of truth is incapable of doubt, only of incorrect interpretation. For the true sage their Knowledge is their living Reality, no more questionable than 2=2=4 and possibly less so.
So to clarify, these three questions are respectively asking the nature, the importance, and the consequences of truth in Buddhism.
It's a good question and much more could usefully be said. The essential point is that Knowledge is not a relative phenomenon. Rather. it is attained by a collapse of the knower-known distinction. Thus the Oracle's advice to 'Know Thyself' since then, apart from trivia, we will know everything there is to know.
Bear in mind that this is in some ways a Mahayana answer. Other traditions pay less attention to logic and metaphysics. In Buddhism we either know or we don't, and while performing calculations may tell us where the knowledge lies and give us confidence in the practice it cannot produce upper-case Knowledge.