What is considered lying in Buddhist (five) precepts?

When information is private, then instead of lying you could say, "I can't tell you", "I'm not allowed to say", or "That's private".

Or you could just not talk about it: and not say anything, or talk about something else.

Part of the definition of "right speech" includes "abstaining from speech", and "not saying" things at the wrong time and/or without affection.

Page 245 of this description of the Monastic Code explains lying in a bit more detail. It says,

A deliberate lie is a statement or gesture made with the aim of misrepresenting the truth to someone else. The K/Commentary, summarizing the long “wheels” in the Vibhaºga, states that a violation of this rule requires two factors:

1. Intention: the aim to misrepresent the truth; and
2. Effort: the effort to make another individual know whatever one wants to communicate based on that aim.

Intention. The aim to misrepresent the truth fulfills this factor regardless of what one’s motives are. Thus “white lies”—made with benevolent intentions (e.g., to a person whose state of mind is too weak to take the truth)—would fall under this rule, so a bhikkhu who wants to shield an emotionally weak person from harsh truths has to be very skillful in phrasing his statements. Also, outrageous lies meant as jokes—to amuse rather than to deceive—would fall under this rule as well, a point we will discuss further in the non-offense section.

Effort. According to the Vibhanga, to misrepresent the truth means to say that one has seen X when one hasn’t, that one hasn’t seen X when one has, or that one has seen X clearly when one is in doubt about the matter. This pattern holds for the other senses—hearing, smell, taste, touch, and ideation—as well. Thus to repeat what one has heard, seen, etc., even if it actually is misinformation, does not count as a misrepresentation of the truth under this rule, as one is truthfully reporting what one has seen, etc. If, however, one says that one believes in such misinformation—when one actually doesn’t—one’s statement would count as a misrepresentation of the truth and so would fulfill this factor.

So apparently a "white lie" intended benevolently to shield someone from harsh truth must be phrased skillfully.

In the case of "the student got kicked out from a University", if you wanted to white-wash that, perhaps you could reply to repeated direct questioning by saying things like,

• "I understand he's left the university"
• "If you want to know why, perhaps you could ask his tutor -- I suppose his tutor would know why"
• "Yes he did explain that to me but it was a private conversation"

The training rules (precepts) are typically more to do with 'acts of commission' (i.e. saying or doing the wrong thing) than 'acts of omission' (i.e. not saying or not doing the right thing). For example if a person were drowning and you could save them but don't, then technically that isn't killing: morally wrong perhaps, but not killing.

Similarly to "be quiet about the truth" isn't the same thing as "tell a lie".

The following is extracted from "One Life Five Precepts" by Venerable Faxun:

Conditions Under Which A Violation Is Considered to Have Occurred

• Object: A human being other than oneself
• Intention: The intent to misrepresent the truth and to deceive
• The Act: The act of communicating the untruth through words or gestures or by being silent
• Consequence: The person comprehends the meaning of the lie. Otherwise, our words are considered idle talk

Exception:

• Unintentional misrepresentation

The use of speech to deceive is obvious, but the body too can be used as an instrument of communication – such as in writing (email, SMS, etc), hand signals, and gestures – all can be used to deceive others. The key element in this transgression is the intention. Therefore, there is no offense if a person misrepresents the truth unintentionally. For example, speaking too quickly and saying one thing while meaning to say another, such as a slip of the tongue.

The Intensity / Severity of Violation

The intensity of violation depends on the content of the untruth and the consequence of the untruthfulness. For example, it is a serious offense when a person, out of greed, lies that he/she has attained arahanthood, and the other person believes him/her.

The aim of observing this precept is to respect truthfulness. Speech is a way of expressing our thoughts. By being mindful with what we say and how we say it, we train ourselves to be more skillful speakers.

By giving up false speech, one becomes a speaker of truth. He does not deceive others, thus becoming a trustworthy and reliable person. Giving up slander, he reconciles those who are divided and brings them closer together. He strengthens friendships by living with love and harmony. Giving up harsh speech, he says what is gentle and pleasant, pleasing to the ear, affectionate and liked by most. Giving up idle chatter, he speaks at the right time in accordance with facts appropriate to the purpose, in accordance with the Dhamma. He speaks words worth treasuring, reasonable, appropriate, discriminating and to the point. (DN 1)

Furthermore, abandoning lying, the disciple of the noble ones abstains from lying. In doing so, he gives freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings. In giving freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings, he gains a share in limitless freedom from danger, freedom from animosity, and freedom from oppression. This is the fourth gift... (AN8.39)

Let's look at the specific examples that you gave. I know that John was kicked out of university because of bad conduct but when asked by a friend, I say, "John probably already moved to another university". All four criteria listed above are fulfilled, so this is considered a lie. According to the commentary, since all the criteria are fulfilled, the "kamma is completed", which means that the intention can potentially cause rebirth in an unwholesome plane of existence.

The Buddha also faced difficult situations when asked questions. In some cases, such as SN 42.2 and SN 42.3, the Buddha said, "Don't ask that question" in other cases, he refused to answer. In AN 5.198, the Buddha gave the criteria for Right Speech as "It is spoken at the right time. It is spoken in truth. It is spoken affectionately. It is spoken beneficially. It is spoken with a mind of good-will."

You asked "Is being honest the same as having wisdom?" Being honest is one aspect of Right Speech. Wisdom (paññā) involves turning the mind inwards through activities such as meditation, studying the Dhamma, teaching the Dhamma and straightening of views. So honesty can arise with or without wisdom. When honesty arises with wisdom there is awareness of the honesty.

The fourth precept in Buddhism pertains to honesty, and breaking it involves lying for personal gain or otherwise. Buddha consistently valued truthfulness as lying can mislead and harm. Occasionally, revealing the truth may not be advisable, but instead of lying, it's better to withhold statements. Liars can commit various wrongdoings, conceal their actions, and craft elaborate excuses. The path advocated is one of honesty, and if speaking the truth is not possible, it's better to remain silent.

Not providing all information, changing the subject or staying silent does not break the precept. But, marketing harmful food as healthy food or selling counterfeits as originals does break the precept.

Understanding the importance of honesty and knowing when to speak,what to speak and whom to speak are all instances of wisdom.