Ils ne sortent jamais sans leur parapluie, même quand il fait un temps magnifique.

Because jamais is the negative word that means never. In French, you usually use ne before the conjugated verb and jamais after it:

Ils ne sortent jamais = They never go out

You do not say ne ... pas jamais here.
Pas would mean not, while jamais already gives the idea of never.

With a simple tense like the present, French normally puts:

• ne before the conjugated verb
• jamais after the conjugated verb

So:

• Ils ne sortent jamais

This is the same pattern you see with other negatives:

• Ils ne sortent pas
• Ils ne sortent plus
• Ils ne sortent jamais

If the verb were in a compound tense, jamais would usually come after the auxiliary:

• Ils ne sont jamais sortis

Sortent is the present indicative, third person plural, from sortir.

Here the present is used for a habitual action or a general truth:

• Ils ne sortent jamais sans leur parapluie
  = This is what they do in general

French uses the present this way just like English does in sentences such as They never go out without their umbrella.

Because leur is singular, so it means their umbrella rather than their umbrellas.

French often uses the singular when the idea is one item per person or when the item is viewed in a general way. So leur parapluie can sound completely natural.

If you wanted to stress that they have multiple umbrellas, you could say leurs parapluies, but that changes the image a little.

So:

• leur parapluie = their umbrella / the umbrella they take with them
• leurs parapluies = their umbrellas

Because leur is already the determiner.

In French, nouns usually need some kind of determiner:

• un parapluie
• le parapluie
• leur parapluie

You do not combine a possessive determiner with another article here, so leur parapluie is complete by itself.

It may feel slightly unusual at first, but it is perfectly normal in French, just as it is in English.

• Ils ne sortent jamais sans leur parapluie
  literally = They never go out without their umbrella

The idea is that they always take their umbrella.

French is happy to use this structure. There is no problem with having both jamais and sans in the same sentence.

Sans means without.

So:

• sortir sans son parapluie = to go out without one’s umbrella

In this sentence, it tells you what they never do: they never go out without it.

A useful comparison:

• Ils sortent avec leur parapluie = They go out with their umbrella
• Ils ne sortent jamais sans leur parapluie = They never go out without their umbrella

The second version is stronger and more idiomatic for this idea.

Quand means when.
Même quand means even when.

The word même adds a sense of contrast or surprise:

• quand il fait beau = when the weather is nice
• même quand il fait beau = even when the weather is nice

So the sentence is emphasizing that they take the umbrella in all cases, including the surprising case of beautiful weather.

The il here is impersonal. It does not refer to a person or thing. It works like English it in weather expressions:

• It is raining
• Il pleut

French often uses il fait in weather phrases:

• il fait beau
• il fait froid
• il fait un temps magnifique

So il is just the normal grammatical subject used in this type of expression.

Both are possible, but il fait un temps magnifique is a very natural weather expression.

It is similar to common French patterns like:

• Il fait beau
• Il fait mauvais
• Il fait un temps splendide

Le temps est magnifique is also understandable and correct, but il fait un temps magnifique sounds especially idiomatic when talking about the weather conditions.

Because magnifique agrees with temps, and temps is singular.

• un temps magnifique = a magnificent weather / wonderful weather

Also, magnifique has the same form in the masculine and feminine singular. The plural adds s in writing:

• un temps magnifique
• des jours magnifiques

So here the singular form is correct because temps is singular.

In careful written French, yes: Ils ne sortent jamais...

In everyday spoken French, many speakers drop ne, especially in informal conversation:

• Ils sortent jamais sans leur parapluie

That is very common in speech, but learners should still know and use the full form ne ... jamais, especially in writing and formal situations.

No. In verbs like this, the -ent ending of the third person plural is usually not pronounced.

So sortent sounds like sort.

Roughly:

• ils sortent → sounds like eel sort

A few pronunciation notes for the sentence:

• Ils = eel
• sortent = the final -ent is silent
• temps is pronounced roughly like tahn
• quand il often links smoothly, almost like kahn-teel

So the spelling looks heavier than the actual pronunciation.