Learn Hardcore Russian: Мой брат очень активный и любит спорт. - My brother is very active and loves sports.

Мой брат очень активный. – uses the full form adjective. Very common and neutral.
Мой брат очень активен. – uses the short form adjective активен.

Short-form adjectives (like активен, рад, готов) are used mainly:

As predicates (after the subject: He is X).
Often in a more formal, bookish, or sometimes more evaluative style.

Here both are correct; очень активный is more colloquial and common in speech, очень активен can sound a bit more formal or written.

Why is it любит and not любить or люблю?

Любить is the infinitive form (to love / to like). In the sentence we need the form that agrees with the subject мой брат (he).

Conjugation of любить in the present:

я люблю – I love
ты любишь – you love (singular, informal)
он / она / оно любит – he / she / it loves
мы любим – we love
вы любите – you love (plural / formal)
они любят – they love

Since мой брат = он (he), we use любит.

What tense and aspect is любит, and why is that form used?

Любит is:

Present tense
3rd person singular
Imperfective aspect of любить

The imperfective aspect is normally used for:

Habits / regular actions
General preferences

Here, любит спорт means likes/loves sport in general (a habitual or general fact), so the imperfective present is exactly what we want. There is also a perfective partner полюбить (to come to love), but that would express the beginning of loving, not a general preference.

Why is it спорт, not спортом, after любит?

Because любить takes its object in the accusative case, and for the inanimate masculine noun спорт, the accusative is the same as the nominative:

Nominative: спорт
Accusative: спорт (no change)

So:

Он любит спорт. – He likes sport.
Она любит музыку. – She likes music. (музыка → музыку in the accusative)

Спортом is the instrumental case, used for example with заниматься:

Он занимается спортом. – He does/practises sport(s).

Why don’t we say спорты (sports) in the plural, like in English?

In Russian, спорт is usually treated as an uncountable, collective noun when you mean sport(s) in general:

Он любит спорт. – He likes sport / sports.
Она занимается спортом. – She does sports.

If you want to talk about specific sports as separate things, you normally name them:

Он любит футбол и теннис. – He likes football and tennis.
Она любит зимние виды спорта. – She likes winter sports.

The bare plural спорты is rare and sounds odd in most everyday contexts.

Could we say Ему нравится спорт instead of Он любит спорт? What’s the difference?

You can say Ему нравится спорт, but there is a nuance difference:

Он любит спорт. – He loves/likes sport.
- Он is the subject.
- Stronger, more emotional; can mean loves.
Ему нравится спорт. – Sport is pleasing to him / He likes sport.
- спорт is the grammatical subject.
- ему is dative (“to him”).
- Often feels a bit milder than любить, more like neutral likes.

Both are correct; choice depends on how strong you want the feeling to be and on style.

Why is и used between активный and любит, and not а?

И and а both can be translated as and, but they are used differently:

и – simple addition, combines similar things:
- Мой брат очень активный и любит спорт.
  → He is very active and (also) likes sport.
а – often contrasts or opposes two things, like but / whereas:
- Мой брат любит спорт, а моя сестра нет.
  → My brother likes sport, but my sister doesn’t.

Here we’re just listing two positive facts about the same person, so и is the natural choice.

Can we change the word order, for example Мой брат любит спорт и очень активный?

You cannot leave it exactly like ...любит спорт и очень активный. After и you need something grammatically parallel:

Мой брат очень активный и любит спорт.
- Predicate 1: очень активный
- Predicate 2: любит спорт

To keep it correct when changing word order, you must keep clear clauses or parallel parts. Examples of correct variations:

Мой брат любит спорт и очень активен.
Мой брат любит спорт, он очень активный.
Он очень активный и любит спорт.

But Мой брат любит спорт и очень активный sounds incomplete; we’re missing a verb or structure after и.

Can we move очень elsewhere, like Мой очень активный брат любит спорт?

Yes, you can move it, but the nuance changes slightly:

Мой брат очень активный и любит спорт.
- Neutral: says two facts about “my brother”.
Мой очень активный брат любит спорт.
- очень активный becomes part of the noun phrase “my very active brother”.
- Feels a bit more like you’re contrasting him with some other brother / person (for example, my very active brother (not the other one) likes sport).

Grammatically both are correct. Очень typically appears right before the word it modifies:

очень активный – very active
очень любит спорт – really loves sport

So Мой брат очень любит спорт is also possible and means My brother really loves sport (emphasising the verb).

Where is the stress in each word of Мой брат очень активный и любит спорт?

Stress pattern:

Мой – one syllable, stress on the whole word.
брат – one syllable, stress on the whole word.
о́чень – stress on the first syllable: О́-чень.
акти́вный – stress on the second syllable: ак-ТИ́В-ный.
и – one syllable, stressed by default in its position.
лю́бит – stress on the first syllable: ЛЮ́-бит.
спорт – one syllable, stress on the whole word.