Я записався до сімейного лікаря.

Because записатися is the verb meaning to sign oneself up, to register, or to book oneself in.

• записав = wrote down / recorded
• записався = signed up / registered / made an appointment

The ending -ся often makes the verb reflexive, so here the idea is that the subject did this for themself.

So:

• Я записав = I wrote down
• Я записався = I signed up / I registered

Yes. It shows that the speaker is male.

In the past tense, Ukrainian verbs agree with gender in the singular:

• записався = a man says it
• записалася = a woman says it

So if a woman were speaking, the sentence would be:

Я записалася до сімейного лікаря.

This is genitive case after the preposition до.

The preposition до often means to, up to, or to see / to go to in certain expressions. After до, the following noun normally goes into the genitive.

Here:

• сімейний лікар = dictionary form, nominative
• до сімейного лікаря = genitive after до

You can see both words change:

• сімейний → сімейного
• лікар → лікаря

So the phrase literally looks like to a family doctor, but idiomatically it means with/to the family doctor depending on context.

Сімейний лікар is a family doctor, meaning a general practitioner / primary care doctor.

It does not mean a doctor for one specific family member only. It is the usual healthcare term for the doctor you regularly go to first for general medical issues.

For an English speaker, GP is often the closest match.

It can depend on context.

записатися до лікаря very commonly means:

• to make an appointment with a doctor
• to book oneself in to see a doctor

But with сімейний лікар, in some contexts it may also suggest:

• to sign up with / register with a family doctor

So the exact meaning depends on the situation around the sentence.

A learner should know that записатися до... often has the general idea of putting yourself on the list to see someone.

Yes, very often.

Ukrainian frequently drops subject pronouns when the verb already makes the meaning clear. So:

• Я записався до сімейного лікаря.
• Записався до сімейного лікаря.

Both can work. The version without Я is very natural if the subject is already understood from context.

You keep Я when you want to:

• emphasize I
• make the subject extra clear
• contrast with someone else

For example: Я записався, а він ні. = I signed up, but he didn’t.

No, Ukrainian word order is fairly flexible.

The neutral order here is:

Я записався до сімейного лікаря.

But other orders are possible for emphasis, for example:

• До сімейного лікаря я записався.
• Я до сімейного лікаря записався.

These can sound more marked or emphasize a particular part of the sentence. For a learner, the original order is the safest and most neutral.

Because лікар is a masculine animate noun, and after до it goes into the genitive singular:

• nominative: лікар
• genitive: лікаря

This -я ending is very common for masculine animate nouns in the genitive singular.

The adjective also has to match it:

• сімейний лікар
• до сімейного лікаря

So both words change together.

Useful related forms are:

• я записуюся = I am signing up / I sign up
• я запишуся = I will sign up / I will make an appointment
• я записався = I signed up / I made an appointment (male speaker)

This also shows an important verb pair:

• записуватися = imperfective
• записатися = perfective

In your sentence, записався is a perfective past form, so it presents the action as completed.

A simple learner-friendly pronunciation guide is:

Ya za-py-SAV-sya do si-MEY-no-ho LI-ka-rya

A few helpful notes:

• я = roughly ya
• -ся is often pronounced close to sya
• г in Ukrainian is usually softer than English g, often closer to a light h sound, so сімейного is roughly si-MEY-no-ho
• stress is important:
  • записався → stress on -сав-
  • сімейного → stress on -мей-
  • лікаря → stress on лі-

No, but до лікаря is one of the most common patterns when you mean to the doctor.

For example:

• йти до лікаря = to go to the doctor
• записатися до лікаря = to make an appointment with the doctor

You may also see other structures in different contexts, but до + genitive is the standard pattern to learn first for this meaning.