Я открыла банку мёда, но крышка плохо открывалась.

Because the verb is in the past tense, and past-tense Russian verbs agree with the subject in gender and number.

• я открыл = I opened (said by a man)
• я открыла = I opened (said by a woman)

So Я открыла tells you the speaker is female.

Because банку is the direct object of открыла.

The dictionary form is банка. After a transitive verb like открыть (to open), a feminine noun of this type usually goes into the accusative singular:

• банка → nominative
• банку → accusative

So:

• Я открыла банку = I opened a jar

Because after a container noun like банка (jar), Russian normally uses the thing inside it in the genitive.

So:

• банка мёда = a jar of honey
• literally, something like a jar of honey

Here:

• мёд = nominative/dictionary form
• мёда = genitive singular

This is very common in Russian:

• чашка чая = a cup of tea
• бутылка воды = a bottle of water
• кусок хлеба = a piece of bread

Because крышка is the subject of the second clause.

In но крышка плохо открывалась, the lid is the thing performing the verb grammatically:

• крышка = the lid
• открывалась = was opening / opened with difficulty

So Russian uses the nominative for крышка.

The -ся here makes the verb work like open in English when we talk about a thing opening itself, rather than someone actively opening it.

Compare:

• Я открыла банку = I opened the jar
  someone did the action to something

• Крышка открывалась = The lid was opening / would open
  the lid is treated as the thing undergoing the action

This reflexive form is very common in Russian for meanings like:

• Дверь открылась = The door opened
• Окно не закрывается = The window won’t close

So открывалась is natural because we are talking about how the lid itself behaved.

This is a very typical Russian aspect contrast.

• открыла is perfective: it presents the action as a completed whole.
• открывалась is imperfective: it focuses on the process, repeated effort, or difficulty.

So the sentence means something like:

• I opened the jar, but the lid was opening badly
• more naturally in English: I opened the jar, but the lid was hard to open

Russian often uses the imperfective when describing how easily or badly something was opening/closing/working, even if the action was eventually completed.

Literally it means was opening badly, but in natural English it usually means:

• didn’t open easily
• was hard to open
• opened with difficulty

So плохо here does not mean the lid opened in a morally bad way or in bad quality; it means the process went with difficulty or not smoothly.

Not really. Russian is describing two different things:

1. The overall result: the jar got opened — Я открыла банку
2. The manner/process: the lid did not open easily — крышка плохо открывалась

So the idea is:

• I managed to open the jar, but the lid was difficult to open

English often uses a different structure, but Russian is perfectly natural here.

You could, but it would change the meaning.

• Я открыла банку мёда = I opened the jar of honey
  completed result

• Я открывала банку мёда = I was opening / used to open / tried opening the jar of honey
  focuses on process, repetition, or context rather than the completed result

In this sentence, открыла is better because the speaker is presenting the opening as an accomplished action.

Because Russian has no articles.

So банку мёда could mean:

• a jar of honey
• the jar of honey

and крышка could mean:

• the lid
• a lid

The exact meaning depends on context. In this sentence, English would normally say the lid, because it is understood to be the lid of that jar.

Yes. Russian word order is more flexible than English word order because case endings show grammatical roles.

The neutral version here is:

• Я открыла банку мёда, но крышка плохо открывалась.

But other orders are possible for emphasis, for example:

• Банку мёда я открыла, но крышка плохо открывалась.
  Emphasizes the jar of honey

• Но плохо открывалась крышка.
  Can emphasize the difficulty or sound more expressive in context

The original order is the most straightforward and neutral.

Yes. In many Russian texts, ё is often written as е, so you may see меда instead of мёда.

But the pronunciation and correct form are:

• мёд
• мёда

For learners, it is helpful to remember that the word is really pronounced with yo:

• мёд = honey

So банку мёда is the same word you may sometimes see written as банку меда.