На нашем факультете сегодня будет лекция, о которой все давно говорят.

With факультет, Russian usually uses на when talking about being at a faculty/department as an institution:

• на факультете = at the faculty / in the department

This is just the normal idiomatic choice in Russian.
So:

• На нашем факультете сегодня будет лекция = There will be a lecture at our faculty/department today

Even though English often uses in, Russian prefers на here.

In this context, факультет usually means a faculty, department, or division within a university, not the English word faculty meaning the teaching staff.

So на нашем факультете is more like:

• at our department
• in our faculty/school
• in our division of the university

The exact English translation depends on the university system being described.

Because нашем has to agree with факультете.

Here is what is happening:

• факультет is masculine
• after на in this meaning, we use the prepositional case
• the prepositional singular of наш with a masculine noun is нашем

So:

• наш факультет = our faculty
• на нашем факультете = at our faculty

The adjective/pronoun changes form to match the noun’s gender, number, and case.

Russian normally does not use есть the way English uses there is / there are in ordinary statements.

To say that something will take place or will happen, Russian often uses:

• будет + noun

So:

• сегодня будет лекция = there will be a lecture today

This sounds natural and idiomatic.

If you said есть лекция, that would usually sound wrong in this context. Russian expresses existence and scheduled events differently from English.

Because лекция is the grammatical subject of будет in this sentence.

Structure:

• Сегодня будет лекция = Today there will be a lecture

Even though English uses there will be, Russian still treats лекция as the noun naming what will exist/happen, so it stays in the nominative:

• лекция = nominative singular

О которой means about which or more naturally which ... about in English.

It introduces a relative clause describing лекция:

• лекция, о которой все давно говорят
• the lecture that everyone has been talking about for a long time

Why this form?

• о = about
• the verb говорить о чём-то means to talk about something
• so the noun/pronoun after о must be in the prepositional case
• since лекция is feminine singular, которая becomes которой

So:

• которая = which (basic form, feminine nominative)
• о которой = about which

Because the relative pronoun is controlled by the preposition о, not by the fact that it refers to лекция.

Compare:

• лекция, которую я слушал = the lecture which I listened to
  
  • here которую is in the accusative
• лекция, о которой все говорят = the lecture about which everyone is talking
  
  • here которой is in the prepositional because of о

So the case of который depends on its role inside the relative clause, not just on the noun it refers to.

This is a very common difference between Russian and English.

Russian often uses the present tense of an imperfective verb to express an action that is:

• ongoing
• repeated
• habitual
• continuing over a period of time

So:

• все давно говорят literally = everyone talks / is talking for a long time
• natural English translation = everyone has been talking about it for a long time

Russian does not need a special form exactly like the English present perfect continuous.

Давно means for a long time or long ago, depending on context.

Here it means the talking has been going on for a long time:

• все давно говорят = everyone has been talking for a long time

It works well with an imperfective verb like говорят, because that verb shows an ongoing or repeated process.

Because о которой все давно говорят is a relative clause attached to лекция.

Russian normally separates relative clauses with commas:

• лекция, о которой все давно говорят

This is similar to written English, where a non-restrictive clause often has commas, but Russian comma rules are generally more regular and mandatory in these structures.

Yes. Russian word order is flexible, though the original sentence is very natural.

Original:

• На нашем факультете сегодня будет лекция, о которой все давно говорят.

Possible variations:

• Сегодня на нашем факультете будет лекция, о которой все давно говорят.
• Лекция, о которой все давно говорят, сегодня будет на нашем факультете.

These all keep roughly the same basic meaning, but the focus changes:

• putting сегодня earlier emphasizes today
• putting лекция earlier emphasizes the lecture
• the original order sounds neutral and smooth

Because все here means everyone or all people, and in Russian it takes a plural verb in this meaning.

So:

• все говорят = everyone is talking / all are talking

Even though English everyone takes a singular verb, Russian uses the plural here.

Yes. Russian has no articles like a and the, so whether лекция is understood as a lecture or the lecture depends on context.

In this sentence, it could feel fairly specific because of the relative clause:

• лекция, о которой все давно говорят = the lecture everyone has been talking about

But in another context, the first part alone:

• Сегодня будет лекция

could simply mean:

• There will be a lecture today

Russian leaves that distinction to context, not articles.