Learn Hardcore Czech: Slunečné počasí je pro prázdniny nejlepší, protože děti můžou být dlouho venku. - Sunny weather is best for the holidays because children can be outside for a long time.

Because počasí is neuter, the correct form is slunečné počasí.
Slunečný počasí is ungrammatical: slunečný is a masculine form, but počasí is neuter.

Why is počasí treated as neuter and does not change its ending?

The noun počasí is one of those Czech nouns that:

end in -í
are neuter
are indeclinable (their form stays the same in all cases)

So you will see počasí in all cases:

nominative: to počasí (the weather)
genitive: bez počasí (without weather)
dative: k počasí (to the weather), etc.

The form never changes; only the words around it (articles, adjectives, pronouns, etc.) change to show case and gender, like slunečné počasí.

Why is it pro prázdniny and not something like na prázdniny?

The preposition pro is used here in the meaning “good/ideal/suitable for”:

Je to nejlepší pro prázdniny. – It is the best *for the holidays.*

Pattern: být (pro někoho / pro něco) dobrý / špatný / vhodný / nejlepší
→ Je to dobré pro děti. – It’s good for children.
→ Je to nejlepší pro prázdniny. – It’s best for the holidays.

Na prázdniny is more like “for the (duration of) the holidays” / “for use during holidays”, or “for going on holidays”:

Balím si věci na prázdniny. – I’m packing my things for the holidays.
Jedeme na prázdniny. – We’re going on holidays.

So:

pro prázdniny – from the point of view of what is good/ideal for that period
na prázdniny – from the point of view of going somewhere / preparing for that period

What exactly does prázdniny mean, and how is it different from dovolená?

Czech has several different words that all translate as “holiday / vacation” in English:

prázdniny
- usually school holidays (summer holidays, Christmas holidays, etc.)
- mostly used for children and students
- always plural: prázdniny (no singular)
dovolená
- time off work (employee vacation)
- feminine singular: dovolená
svátky
- (public, religious, or family) holidays / feast days
- e.g. Christmas, Easter

In your sentence, prázdniny fits well because it talks about children having free time, like school summer holidays.

Is the word order Slunečné počasí je pro prázdniny nejlepší fixed, or can it be changed?

The word order is not strictly fixed; Czech is quite flexible. All of these are grammatically correct:

Slunečné počasí je pro prázdniny nejlepší.
Pro prázdniny je slunečné počasí nejlepší.
Nejlepší pro prázdniny je slunečné počasí.

Differences are mostly about emphasis / what is new information:

Starting with Slunečné počasí makes “sunny weather” the topic:
We are talking about sunny weather and saying it is the best for holidays.
Starting with Pro prázdniny puts more focus on the holidays:
For the holidays (as a period), sunny weather is what’s best.

In normal neutral speech, your original version is perfectly natural and common.

Why is there a comma before protože?

Protože (“because”) introduces a subordinate clause – it explains the reason:

main clause: Slunečné počasí je pro prázdniny nejlepší
subordinate clause: protože děti můžou být dlouho venku

In Czech, a comma is required before most subordinating conjunctions, including:

protože (because)
když (when, if)
že (that)
aby (so that), etc.

So the comma in
Slunečné počasí je pro prázdniny nejlepší, protože děti můžou být dlouho venku.
is obligatory in standard written Czech.

Why is it můžou and not mohou? Are both correct?

Both můžou and mohou are correct forms of the 3rd person plural of moci (can, to be able to):

mohou – more formal / standard, typical in writing, official style
můžou – more colloquial / everyday speech, very common in spoken Czech

In a normal, conversational sentence about kids and holidays, můžou sounds very natural.
If you were writing a formal essay or official text, you might prefer mohou:

Děti mohou být dlouho venku. (formal)
Děti můžou být dlouho venku. (everyday speech)

Why is it děti můžou and not something like a singular form?

Even though děti ends with -i, it is grammatically plural:

dítě – one child (neuter singular)
děti – children (plural)

So the verb must also be in the 3rd person plural:

Dítě může být venku. – The child can be outside.
Děti můžou / mohou být venku. – Children can be outside.

Using a singular verb form (děti může) would be incorrect.

Why does Czech say můžou být dlouho venku instead of something like “can stay”?

Czech often uses být (to be) where English uses stay:

být venku – literally “to be outside”, but usually translated as “to be / stay outside”

So:

Děti můžou být dlouho venku.
literally: Children can be a long time outside.
natural English: Children can stay outside for a long time.

You can also say:

Děti můžou zůstat dlouho venku. – Children can stay outside for a long time.

Both are correct, but být venku is very common and slightly simpler / more neutral.

What is the difference between venku and ven?

This is a classic Czech pair:

venku – location: where something/someone is (outside)
- Jsem venku. – I am outside.
- Děti jsou venku. – The children are outside.
ven – direction: where to something/someone goes (out)
- Jdu ven. – I’m going out.
- Pusť mě ven. – Let me out.

In your sentence, we talk about being outside (a state), not moving out, so venku is correct:

Děti můžou být dlouho venku. – Children can be outside for a long time.

Why is dlouho used, and not something like dlouhý čas venku?

Dlouho is an adverb meaning “for a long time”.
It is the natural way to express duration with verbs:

čekat dlouho – to wait for a long time
spát dlouho – to sleep for a long time
být dlouho venku – to be outside for a long time

Phrases like dlouhý čas venku are grammatically possible but sound unnatural / too literal in this context.
Native speakers almost always use dlouho here:

Děti můžou být dlouho venku. – Children can be outside for a long time.