Learn Hardcore Portuguese (Brazil): Na segunda-feira eu chegaria mais cedo se não houvesse trânsito. - On Monday I would arrive earlier if there were no traffic.

By default, na segunda-feira in your sentence refers to a specific Monday (usually understood from context, like “this coming Monday” or “last Monday”).

To talk about Mondays in general, you would more often use something like:

Às segundas(-feiras) eu chego mais cedo se não houver trânsito.
(On Mondays I arrive earlier if there is no traffic.)

Here às segundas (plural) suggests a regular habit.

What tense/mood is chegaria, and why is it used here?

Chegaria is the conditional (also called the future of the preterite) of chegar.

chegar – to arrive
chegaria – I would arrive

It is used because the sentence is hypothetical, depending on a condition:

Eu chegaria mais cedo se não houvesse trânsito.
I would arrive earlier if there were no traffic.

Portuguese typically pairs:

conditional in the main clause (chegaria)
with imperfect subjunctive in the se-clause (se não houvesse)

Could I say eu vou chegar mais cedo se não houver trânsito instead? What changes?

Yes, that is also correct, but the meaning changes slightly:

Eu chegaria mais cedo se não houvesse trânsito.
→ More hypothetical/unreal, often contrary to fact or unlikely.
I would arrive earlier if there were no traffic (but there usually is).
Eu vou chegar mais cedo se não houver trânsito.
→ A real future condition; you consider it possible.
I’m going to arrive earlier if there’s no traffic.

So chegaria / houvesse = hypothetical;
vou chegar / houver = real future condition.

Why is it houvesse and not something like havia or há?

Houvesse is the imperfect subjunctive of haver.

haver (impersonal, as “there to be”)
- há trânsito – there is traffic
- havia trânsito – there was traffic
- se não houvesse trânsito – if there were no traffic

You need the subjunctive because this is a hypothetical condition introduced by se:

Se não houvesse trânsito, eu chegaria mais cedo.
If there were no traffic, I would arrive earlier.

Using se não há trânsito or se não havia trânsito here would sound wrong or at least very odd, because it mixes a real/indicative form with a conditional structure that calls for the subjunctive.

How is houvesse formed from haver?

Houvesse is the 3rd person singular imperfect subjunctive of haver.

Imperfect subjunctive pattern (for regular -ar/-er/-ir verbs) is often built from the third person plural of the preterite:

haver → preterite 3rd plural: houveram
root: houver-
add endings: -sse, -sse, -ssemos, -ssem

So you get:

eu houvesse
tu houvesses
ele / ela / você houvesse
nós houvéssemos
eles / elas / vocês houvessem

In the impersonal sense (“there to be”), only ele form appears, but it doesn’t agree with anything:

houvesse trânsito – literally: there were traffic (always 3rd person singular).

Could I use ter instead of haver, like se não tivesse trânsito?

Yes, in Brazilian Portuguese ter is extremely common in speech instead of impersonal haver.

So you could say:

Eu chegaria mais cedo se não tivesse trânsito.

This is very natural in everyday conversation and informal writing.

Subtle points:

haver is more formal and traditional for the impersonal “there is/are”.
ter in this impersonal sense is very common, especially in Brazil.

Both are widely understood and accepted, especially in speech.

Why is there não before houvesse? Could it go somewhere else?

Não is the regular negation word (not), and in Portuguese it normally comes right before the verb:

se houvesse trânsito – if there were traffic
se não houvesse trânsito – if there were no traffic

You can’t move não to another position (like se houvesse não trânsito); that would be wrong in Portuguese. The standard pattern is:

não + verb → não houvesse

What does mais cedo mean exactly? Do I need to say “earlier than…”?

Mais cedo means earlier.

In this sentence, the comparison (earlier than usual / earlier than planned) is understood from context, so you don’t need to say:

mais cedo do que… (earlier than …)

Examples:

Eu chego cedo. – I arrive early.
Eu chego mais cedo. – I arrive earlier (than some other time/situation).

Do I need a comma before se não houvesse trânsito?

Yes, the comma is standard and recommended here:

Na segunda-feira eu chegaria mais cedo, se não houvesse trânsito.

You are separating the main clause from the conditional clause:

Main clause: Na segunda-feira eu chegaria mais cedo
Conditional clause: se não houvesse trânsito

If you invert the order, the comma is obligatory:

Se não houvesse trânsito, eu chegaria mais cedo.

Can I leave out eu and just say Na segunda-feira chegaria mais cedo se não houvesse trânsito?

Yes, you can omit eu:

Na segunda-feira chegaria mais cedo se não houvesse trânsito.

Portuguese is often a pro-drop language: subject pronouns are frequently omitted because the verb ending indicates the person:

chegaria here clearly refers to eu (I).

Leaving out eu sounds slightly more formal or written, but it’s grammatically correct and common.

Could I change the order of the clauses, like Se não houvesse trânsito, na segunda-feira eu chegaria mais cedo?

Yes, that is perfectly correct:

Se não houvesse trânsito, na segunda-feira eu chegaria mais cedo.

All these are acceptable and mean the same thing, with only slight rhythm/stylistic differences:

Na segunda-feira eu chegaria mais cedo se não houvesse trânsito.
Eu chegaria mais cedo na segunda-feira se não houvesse trânsito.
Se não houvesse trânsito, eu chegaria mais cedo na segunda-feira.

The important points are:

Keep se
- subjunctive together (se não houvesse trânsito).
Use a comma when the se-clause comes first.