Learn Hardcore Russian: Сегодня моя коллега ведёт совещание, а в конце начальница делает ей комплимент за ясный план. - Today my colleague is running a meeting, and at the end the female boss gives her a compliment for a clear plan.

Сегодня моя коллега будет вести совещание… (will be leading) or more “completed”/result-focused:
Сегодня моя коллега проведёт совещание… (will conduct and finish it)
…начальница сделает ей комплимент… (will give her a compliment)

What does ведёт совещание mean literally, and why use вести here?

вести literally means to lead or to conduct.
So вести совещание is a very common collocation meaning to run/lead a meeting.

Other natural options exist, with slightly different feel:

проводить совещание = to hold/conduct a meeting (often more “organizational”)
руководить совещанием = to preside over the meeting (more formal/“in charge”)

Why is it ведёт with ё, and how is it pronounced?

It’s the 3rd-person singular present of вести:

он/она ведёт = he/she leads

ё is pronounced yo: ve-DYOT (stress on the second syllable).
In many texts ё is often written as е (ведет), but pronunciation stays ведёт.

How do we know коллега is female if коллега can refer to a man too?

коллега is a “common gender” noun: it can describe a man or a woman.
Here it’s clearly female because of agreement:

моя коллега (not мой коллега)

So the pronoun/adjective tells you the person’s gender.

What case is совещание in, and why doesn’t its form change?

It’s in the accusative because it’s the direct object of ведёт (leads what?).
But совещание is neuter inanimate, and for many neuter inanimate nouns:

nominative = accusative

So совещание looks the same in both cases.

Why is there a comma before а, and what does а mean here?

In Russian, you normally put a comma before coordinating conjunctions like а when they connect two clauses:

…ведёт совещание, а … делает…

а often means and/but with a contrast or shift of focus (like “and meanwhile / whereas / but”).
Here it feels like: one action happens, and then another action follows.

Does в конце mean “at the end (of the meeting)”? Shouldn’t it be в конце совещания?

в конце by itself means at the end and the context can supply “of what.”
If you want to be explicit, you can absolutely say:

в конце совещания = at the end of the meeting

Both are correct; the longer version is clearer.

Why is it начальница and not начальник, and what’s the nuance?

начальник is the general word for boss/supervisor and is often used for both genders in practice.
начальница explicitly marks a female boss.

So choosing начальница highlights that the boss is a woman (and it matches the feminine verb form if you were in past tense).

Why is it делает ей комплимент—why is ей in the dative?

Because the person receiving the compliment is an indirect object:

делать комплимент кому? = to pay a compliment to whom?

So:

ей (dative of она) = to her

Common pattern:

Он сделал мне комплимент. = He paid me a compliment.

Why is it за ясный план, and what case is ясный план?

за meaning for (as a reason / in praise of) takes the accusative:

за + accusative = for, in return for, because of (positive/neutral reason)

So ясный план is accusative, but for an inanimate masculine noun like план, the accusative looks like the nominative:

ясный план (same form)

Note: this за is not the same as из-за (“because of” usually with a negative/causal nuance).