Learn Hardcore Czech: Moje kolegyně se směje, ale říká, že projekt není příliš dlouhý a že má ráda práci, kde se učí nové věci. - My female colleague is laughing, but she says that the project is not too long and that she likes work where she learns new things.

The dictionary form is smát se = to laugh.
Many Czech verbs are reflexive verbs, whose meaning changes when you add se or si.
For smát, you almost always use it as smát se. Without se, smát sounds incomplete or archaic.

So Moje kolegyně se směje simply means My colleague is laughing. It does not imply that she is laughing at herself.

Why is it Moje kolegyně se směje, and not Moje kolegyně směje se? Where does se go?

Czech has special little words called clitics (like se, si, short forms of pronouns, etc.), and they usually go in second position in the clause.

The first stressed unit here is Moje kolegyně.
The clitic se normally comes right after that first unit.
So the natural word order is: Moje kolegyně se směje, not Moje kolegyně směje se.

Putting se after the verb is possible in some special emphatic or poetic contexts, but as a learner, stick to second position: [first stressed word/group] + se + verb.

What exactly does říká, že… do? Why do we need že here?

Říkat = to say / to tell. When you report what someone says, you usually introduce the content with že (= that).

říká, že projekt není příliš dlouhý
= she says (that) the project is not too long

In English, that can be dropped: She says the project is not too long.
In Czech, you normally keep že to start this kind of subordinate clause. Removing že is unusual and often sounds incomplete or wrong.

Why is there a comma before ale and before že?

Two different rules:

Comma before ale
- Ale = but is a coordinating conjunction.
- Czech always writes a comma before ale when it connects two clauses:
  - Moje kolegyně se směje, ale říká…
Comma before že
- Že introduces a subordinate clause (reported speech / object clause).
- Czech always separates this with a comma:
  - říká, že projekt není…
  - a že má ráda práci…

So both commas are required by standard Czech punctuation rules.

Why is it projekt není příliš dlouhý and not something like projekt není moc dlouhý? Do příliš and moc mean the same?

Both příliš and moc can mean too (much), but there are nuances:

příliš dlouhý = too long / excessively long
- More neutral or slightly formal.
- With negation není příliš dlouhý often softens it to not very long / not particularly long.
moc dlouhý = too long (colloquial, more emotional)
- není moc dlouhý = isn’t too long (sounds more conversational).

In this sentence, není příliš dlouhý sounds fairly neutral and polite, fitting written style.

Why is it má ráda práci and not just ráda práci? What does mít rád mean?

Mít rád (for men) / mít ráda (for women) means to like (people, things, activities).

mít = to have
rád / ráda / rádo / rádi = an adjective meaning something like glad / fond

So má ráda práci literally is she has [it] gladly, the work → idiomatically she likes the work.

You must use mít here; ráda práci alone is ungrammatical as a main predicate.
Correct patterns:

Má ráda práci. = She likes work / her job.
Ráda pracuje. = She likes working (she gladly works).

Both are common, but they are structured differently.

Why is it má ráda (with -a) and not má rád?

The form of rád agrees with the gender and number of the person who likes something:

masculine singular: mám rád
feminine singular: mám ráda
neuter singular: mám rádo (rare, mainly for children/animals in special contexts)
plural (mixed / masculine animate): máme rádi
feminine plural: máme rády

Since kolegyně is a female colleague, she says:

Moje kolegyně má ráda práci.

A man would say:

Můj kolega má rád práci.

Why is it kolegyně and not kolega? What’s the difference?

Both mean colleague, but they differ in gender:

kolega = male colleague (masculine)
kolegyně = female colleague (feminine)

Czech marks grammatical gender in nouns, and that affects agreement:

Moje kolegyně se směje. Má ráda práci. (feminine → ráda)
Můj kolega se směje. Má rád práci. (masculine → rád)

Why is it práci and not práce in má ráda práci?

Práce is the base form (work, job), feminine:

Nominative (subject): práce
Accusative (direct object): práci

In má ráda práci:

The verb phrase má ráda needs a direct object: likes what? → práci.
Direct objects usually take the accusative.

So práce would be correct as a subject (e.g. Práce je zajímavá = The work is interesting), but as an object, you need práci.

In a že má ráda práci, kde se učí nové věci, who is the subject of má ráda and se učí if there is no pronoun ona?

The subject is still Moje kolegyně; Czech normally drops subject pronouns when they’re clear from context.

The structure is:

Moje kolegyně se směje, ale říká, že
- (ona) má ráda práci, kde (ona) se učí nové věci.

The ona is understood:

The same person (your colleague) both likes the work and learns new things in that work.
Czech relies heavily on verb endings and context instead of repeating já / ty / on / ona all the time.

Why is it kde se učí nové věci? Doesn’t kde just mean “where”? Can it mean “where (she) learns … / in which (she) learns …”?

Yes, kde usually means where, but it also works as a relative pronoun similar to English where in:

I like work where I learn new things.

So:

práci, kde se učí nové věci
= a job where she learns new things
= a job in which she learns new things

More formal alternatives would be práci, ve které se učí nové věci, but kde is very common and natural.

What’s the difference between učit and učit se? Why is it kde se učí nové věci, not kde učí nové věci?

učit někoho / něco = to teach (someone / something)
- učím děti angličtinu = I teach children English.
učit se něco = to learn (something)
- učím se angličtinu = I’m learning English.

In the sentence, your colleague is learning, not teaching, so the verb needs the reflexive form:

práci, kde se učí nové věci
= work where she learns new things

If you said kde učí nové věci, it would mean where she teaches new things (she is the teacher).

Why is it nové věci? What are these forms?

věc = thing, feminine singular
věci = things, nominative/accusative plural

Nový is the adjective new:

masculine singular: nový
feminine singular: nová
neuter singular: nové
plural for all genders in accusative (non-animate) and nominative: nové

Here we have nové věci:

věci = feminine plural, accusative (direct object of učí se)
nové agrees in number (plural) and case (accusative) → nové věci = new things.