Learn Hardcore Portuguese (Portugal): Eu fico mais seguro quando estudo com o Pedro.

Eu sou seguro – I am (by nature) a secure/confident person. (permanent trait)
Eu estou seguro – I am safe / I feel safe (right now). (temporary state)
Eu fico mais seguro – I become / get safer / more confident (when something happens).

In Eu fico mais seguro quando estudo com o Pedro, the idea is: because I study with Pedro, my level of security/confidence increases. That change is why ficar is the natural choice.

Does ficar here mean to stay or to become?

Here it means to become / to get, not to stay.

Ficar has several common meanings:

to become / to get
- Fico nervoso antes dos exames. – I get nervous before exams.
- Fico mais seguro quando estudo com o Pedro. – I get / feel safer when I study with Pedro.
to stay / to remain
- Fico em casa hoje. – I’m staying at home today.
to be located
- A escola fica perto da estação. – The school is (located) near the station.

In your sentence, meaning 1 (change of state) is the right one.

If I am a woman, should I say segura instead of seguro?

Yes.

Adjectives agree in gender with the person they describe:

A man: Eu fico mais seguro quando estudo com o Pedro.
A woman: Eu fico mais segura quando estudo com o Pedro.

Only seguro/segura changes. The rest of the sentence stays the same.

Is mais seguro like safer in English? How do comparatives work here?

Yes, mais seguro corresponds to safer / more secure / more confident.

For most adjectives, Portuguese forms the comparative with mais + adjective:

mais alto – taller
mais rápido – faster
mais caro – more expensive
mais seguro – safer / more secure

So:

Eu fico seguro. – I am / become safe.
Eu fico mais seguro. – I am / become safer (than before / in other situations).

There is no special -er ending like in English.

Could I say Eu sinto-me mais seguro instead of Eu fico mais seguro?

Yes, but the nuance changes slightly.

Eu fico mais seguro – I get / become safer/more confident (studying with Pedro makes my level change).
Eu sinto-me mais seguro – I feel safer (you’re focusing more on your subjective feeling).

In many contexts they are both possible, but ficar + adjective is very common and sounds a bit more neutral and natural for this kind of sentence.

Why is there an o before Pedro? Why com o Pedro and not just com Pedro?

In European Portuguese, it is very common to use the definite article with people’s names:

o Pedro, a Maria, o João, a Ana

So:

Estudo com o Pedro. – I study with Pedro.
Vou falar com a Maria. – I’m going to talk to Maria.

In Portugal, saying com Pedro (without o) is not wrong, but com o Pedro is more natural in everyday speech. In Brazilian Portuguese the article before names is less consistent and often omitted.

How does the article change with different names? For example, with Maria?

The article agrees in gender and number with the name:

Masculine singular: o Pedro, o João, o Miguel
Feminine singular: a Maria, a Ana, a Joana
Masculine plural: os Pedros (several people called Pedro)
Feminine plural: as Marias (several people called Maria)

So you would say:

Eu estudo com a Maria. – I study with Maria.
Eu estudo com o Pedro. – I study with Pedro.

Can I say Quando eu estudo com o Pedro, eu fico mais seguro instead? Is that correct?

Yes, that is correct and perfectly natural:

Quando estudo com o Pedro, fico mais seguro.
Quando eu estudo com o Pedro, eu fico mais seguro.

Both are grammatically fine. The version with eu repeated tends to give a bit more emphasis to I (you, personally) but in many contexts it’s just stylistic. In Portuguese, omitting subject pronouns is very common because the verb ending already shows the subject.

Why can eu be omitted in eu estudo and eu fico? When do people drop it?

Portuguese is a “null subject” language: the verb ending shows the subject, so the pronoun is often dropped:

Eu estudo. → Estudo. – I study.
Eu fico mais seguro. → Fico mais seguro. – I get safer.

People usually add the pronoun for:

emphasis: Eu fico mais seguro, not you.
contrast: Eu estudo, mas ela não estuda.
clarity when context is confusing.

In your sentence, all of these are possible and natural:

Eu fico mais seguro quando estudo com o Pedro.
Fico mais seguro quando estudo com o Pedro.
Eu fico mais seguro quando eu estudo com o Pedro.

Does quando estudo mean when I study, whenever I study, or if I study?

It most naturally covers when / whenever I study, and can be close to if I study in a habitual sense.

Quando estudo com o Pedro, fico mais seguro.
– When I study with Pedro, I get safer.
– Whenever I study with Pedro, I get safer.

It expresses a regular or general condition in the present, much like English when I study in sentences like When I study with him, I understand better. It is not the conditional se (if), but in practice it often describes a similar “whenever this happens, that happens” relationship.

Is the word order fixed, or can I move the clause starting with quando to the front?

You can move it; both orders are normal:

Eu fico mais seguro quando estudo com o Pedro.
Quando estudo com o Pedro, eu fico mais seguro.

Just like in English:

I feel safer when I study with Pedro.
When I study with Pedro, I feel safer.

The meaning doesn’t change; the choice is stylistic.

How do you pronounce Eu fico mais seguro quando estudo com o Pedro in European Portuguese?

Approximate European Portuguese pronunciation (very rough guide):

Eu – like “eh-oo” (often almost just “eu” [eu])
fico – “FEE-koo”
mais – “maish” (final s sounds like sh)
seguro – “sɨ-GOO-roo” (first e is a very reduced sound, like a quick uh)
quando – “KWAHN-doo”
estudo – “(ɨ)SH-TU-doo” (initial e is reduced and often barely audible; es- before consonant often sounds like sh)
com – “kong” (final m gives a nasal sound)
o – “oo”
Pedro – “PEH-droo” (the d is often a bit softer than in English)

Spoken quickly, it flows something like:

“Eu FEE-koo maish sɨ-GOO-roo KWAHN-doo (ɨ)SH-TU-doo kong oo PEH-droo.”