Bei Regen ist der Sicherheitsabstand noch wichtiger als sonst.

Bei Regen means when it is raining / in rainy conditions / in the rain in a general sense.

German bei is often used for conditions or circumstances:

• bei Hitze = when it’s hot
• bei Dunkelheit = in darkness
• bei Regen = when it’s raining

Im Regen usually means physically in the rain, as in being out there getting wet:

• Ich war im Regen draußen. = I was outside in the rain.

So in this sentence, bei Regen is about the driving condition, not physical location.

Because Regen is being used generically, meaning rain as a general weather condition.

German often leaves out the article with nouns in set expressions like this:

• bei Regen
• bei Schnee
• bei Nebel

This is similar to how English often says in rain or in foggy conditions, rather than in the rain when speaking generally.

If you were talking about a specific rain event, an article might appear in another kind of sentence, but here the article-less form is the normal one.

Because German main clauses follow the V2 rule: the finite verb must come in second position.

Here, Bei Regen comes first as one whole idea, so the verb ist must come next:

• Bei Regen | ist | der Sicherheitsabstand | noch wichtiger als sonst

Even though der Sicherheitsabstand is the subject, it comes after the verb because Bei Regen has been placed first.

A more neutral order would be:

• Der Sicherheitsabstand ist bei Regen noch wichtiger als sonst.

Both are correct.

Der Sicherheitsabstand is the subject of the sentence, so it is in the nominative case.

The noun Sicherheitsabstand is masculine, so its nominative singular article is der.

That gives:

• der Sicherheitsabstand = nominative singular masculine

You can tell it is the subject because it is the thing being described as more important.

Sicherheitsabstand is a German compound noun:

• Sicherheit = safety
• Abstand = distance

So literally it means safety distance.

In driving contexts, it usually means:

• safe following distance
• stopping distance / distance you keep from the car in front

A useful thing to know about German compounds: the last part determines the gender.
Since Abstand is masculine (der Abstand), the whole compound is masculine:

• der Sicherheitsabstand

Because the sentence is making a comparison:

• important in normal conditions
• more important when it rains

So German uses the comparative of wichtig:

• wichtig = important
• wichtiger = more important

That matches the later part:

• als sonst = than usual / than otherwise

So:

• noch wichtiger als sonst = even more important than usual

In standard German, most common adjectives form the comparative with -er:

• klein → kleiner
• schnell → schneller
• wichtig → wichtiger

So wichtiger is the normal form.

Using mehr wichtig would sound unnatural here. German usually prefers the built-in comparative form rather than mehr + adjective.

Here noch means something like even.

So:

• wichtiger = more important
• noch wichtiger = even more important

This is a very common use of noch with comparatives:

• noch besser = even better
• noch größer = even bigger
• noch wichtiger = even more important

It does not mean still in this sentence.

German uses als after a comparative:

• größer als = bigger than
• schneller als = faster than
• wichtiger als = more important than

So wichtiger als sonst is the normal pattern.

Sonst here means otherwise / usually / under other circumstances.
So als sonst means:

• than usual
• than otherwise

In this sentence, sonst means in other situations or normally.

So:

• wichtiger als sonst = more important than it normally is

It does not literally mean one single English word in every context. Sonst can mean:

• otherwise
• else
• normally / in other cases

Here the best sense is than usual or than under normal conditions.

Because it comes after the verb ist and is functioning as a predicate adjective.

Predicate adjectives in German do not take adjective endings:

• Der Abstand ist wichtig.
• Der Abstand ist wichtiger.

Adjective endings appear when the adjective comes before a noun:

• ein wichtiger Abstand
• der wichtige Abstand

So in this sentence, wichtiger has no extra ending because it is part of:

• ist ... wichtiger

Yes, absolutely.

That version is also correct:

• Der Sicherheitsabstand ist bei Regen noch wichtiger als sonst.

The difference is mainly emphasis:

• Bei Regen ist der Sicherheitsabstand ...
  puts the focus first on the condition: when it rains

• Der Sicherheitsabstand ist bei Regen ...
  starts more directly with the topic: the safety distance

German often moves elements to the first position for emphasis, while still keeping the verb in second position.