Мой брат надел клетчатую рубашку, а я выбрала полосатую футболку.

Because брат is a masculine noun in Russian, and the possessive word мой must agree with it.

• мой брат = my brother
• моя сестра = my sister
• моё письмо = my letter
• мои друзья = my friends

So the form of my changes depending on the gender and number of the noun.

Надел is the masculine past tense of надеть, which means to put on an item of clothing.

In this sentence:

• Мой брат надел клетчатую рубашку = My brother put on a plaid/checkered shirt.

A very common learner question is the difference between надеть and одеть:

• надеть = to put something on oneself or onto someone/something
  
  • надеть рубашку
• одеть = to dress a person
  
  • одеть ребёнка

So here надел рубашку is exactly the right choice, because the brother put on a shirt.

Because the speaker is understood to be female.

Russian past tense verbs agree with gender in the singular:

• я выбрал = I chose (male speaker)
• я выбрала = I chose (female speaker)

So the sentence tells us that the person saying я is a woman or girl.

Because both noun phrases are in the accusative case, which is used here for the direct object of the verbs.

The verbs надел and выбрала both act on something:

• put on what? → рубашку
• chose what? → футболку

Both рубашка and футболка are feminine singular nouns, and in the accusative singular they change like this:

• рубашка → рубашку
• футболка → футболку

Their adjectives must agree:

• клетчатая → клетчатую
• полосатая → полосатую

So the whole phrases change together.

А often shows contrast or a comparison between two parts of a sentence.

Here the idea is:

• My brother put on a plaid shirt, whereas / and as for me I chose a striped T-shirt.

So а works better than и because the sentence is comparing two people and their different choices.

Very roughly:

• и = and
• а = and/but/whereas, with contrast or topic shift

It does not necessarily mean a strong but; often it is just a gentle contrast.

Because the sentence presents both actions as completed events.

• надел = put on, completed
• выбрала = chose, completed

Russian often uses the perfective aspect when talking about a single finished action in the past.

If you used imperfective forms, the meaning would change:

• надевал = was putting on / used to put on
• выбирала = was choosing / used to choose

So the sentence is not describing an ongoing process. It is describing what each person ended up doing.

Not strictly, but it is very natural here because it helps create the contrast:

• Мой брат надел клетчатую рубашку, а я выбрала полосатую футболку.

The я emphasizes as for me / I, on the other hand.

Russian often omits subject pronouns when they are clear from the verb form, but pronouns are commonly included for:

• contrast
• emphasis
• clarity

Without я, the sentence would sound less balanced.

Yes. Russian word order is fairly flexible, though changing it affects emphasis.

Neutral order here is:

• Мой брат надел клетчатую рубашку, а я выбрала полосатую футболку.

Other possible orders could highlight different parts:

• Клетчатую рубашку надел мой брат, а я выбрала полосатую футболку.
  Emphasis on the plaid shirt.
• Мой брат надел рубашку клетчатую...
  Possible in some contexts, but less neutral and usually less natural for a learner.

For everyday use, the original word order is a good standard model.

Because the sentence is focusing on two different actions:

• the brother put on a shirt
• the speaker chose a T-shirt

Russian is not trying to force the same action in both parts. It is just describing what happened from each person’s point of view.

This is perfectly natural. It may imply something like:

• he already got dressed
• I was deciding what to wear

So the contrast is not only between the clothes, but also between the actions.

A helpful stress guide is:

• мой брат наде́л клетча́тую руба́шку, а я вы́брала полоса́тую футбо́лку

A few notes:

• наде́л — stress on -дел
• клетча́тую — stress on ча
• руба́шку — stress on ба
• вы́брала — stress on the first syllable
• полоса́тую — stress on са
• футбо́лку — stress on бол

Stress is very important in Russian, because it is not always predictable and wrong stress can sound unnatural.

Yes, Russian can express these ideas in more than one way.

You may hear:

• клетчатая рубашка = plaid/checkered shirt
• рубашка в клетку = shirt with a check/plaid pattern

and

• полосатая футболка = striped T-shirt
• футболка в полоску = T-shirt with stripes

The sentence uses the adjective forms клетчатую and полосатую, which are completely natural and common. For a learner, they are useful because they clearly show adjective agreement with the noun.