Ко мне подплыла большая рыба.

The preposition is basically к (to, toward), but before some word combinations Russian uses ко instead because it is easier to pronounce.

So:

• к дому
• к брату
• but ко мне
• ко всему
• ко вторнику in some contexts

This is mostly a pronunciation issue, not a meaning change. In your sentence, ко мне simply means to me / up to me.

Because к / ко requires the dative case.

The pronoun я changes like this:

• nominative: я = I
• genitive/accusative: меня
• dative: мне
• instrumental: мной / мною
• prepositional: мне

So:

• ко мне = to me
• к тебе = to you
• к нему = to him

Подплыла means something like swam up to, came swimming up to, or approached by swimming.

It comes from:

• плыть = to swim / to float / to move through water
• prefix под- = here it gives the idea of approaching or coming up to
• past tense feminine ending -ла

So подплыла is not just swam in a general sense. It specifically suggests movement toward someone or something.

In the past tense, Russian verbs agree in gender and number with the subject.

The subject here is рыба (fish), and рыба is a feminine noun in Russian.

So:

• masculine: подплыл
• feminine: подплыла
• neuter: подплыло
• plural: подплыли

Because рыба is feminine, the verb must be подплыла.

Because adjectives must agree with the noun they describe in gender, number, and case.

The noun is рыба, which is:

• feminine
• singular
• nominative case

So the adjective must also be feminine singular nominative:

• большой = dictionary form / masculine-like citation form
• большая рыба = a big fish

Compare:

• большой кот
• большая рыба
• большое озеро
• большие рыбы

Because рыба is the subject of the sentence — the thing doing the action.

In Ко мне подплыла большая рыба, the fish is the one that swam up. That makes большая рыба the subject, so it stays in the nominative case.

Meanwhile:

• ко мне is a prepositional phrase with dative
• большая рыба is nominative because it is the subject

Both are possible, but the emphasis changes.

• Большая рыба подплыла ко мне = more neutral, straightforward: A big fish swam up to me
• Ко мне подплыла большая рыба = puts focus first on to me, and often sounds more vivid or scene-setting, like Up to me swam a big fish

Russian word order is much freer than English word order because case endings show grammatical roles. So changing the order often changes focus or style, not the core meaning.

Yes. Подплыла is perfective.

That matters because perfective verbs usually present the action as a completed event or a single whole action:

• подплывала = was swimming up / used to swim up / approached repeatedly or as a process
• подплыла = swam up, arrived near

In this sentence, the perfective form fits well because it describes a completed event: the fish came up to the speaker.

Both can be translated as swam to / arrived by swimming, but they are not exactly the same.

• подплыла = came up close to, approached
• приплыла = arrived by swimming, reached a destination

So:

• Ко мне подплыла большая рыба emphasizes that the fish came up near me.
• Ко мне приплыла большая рыба is possible in some contexts, but it can sound more like the fish arrived to me as a destination, rather than specifically swimming up close.

For this sentence, подплыла is very natural because it highlights approach.

Russian has no articles like a or the.

So большая рыба can mean either:

• a big fish
• the big fish

You figure it out from context.

In an isolated sentence like this, English will usually translate it as a big fish, because it sounds like new information being introduced.

Yes. Рыба can mean:

• a fish as an animal
• fish as food
• fish in a general category

In this sentence, because it swam up, it clearly means a live fish.

Russian often relies on context for this, just like English does with the word fish.

Because Russian often builds that meaning into the verb prefix.

English uses:

• swam up to

Russian uses:

• под-
  • плыла → подплыла

This is very common in Russian. Prefixes add direction or nuance to motion verbs:

• войти = go in / enter
• выйти = go out
• подойти = come up to
• отойти = move away
• подплыть = swim up to

So instead of a separate word like up, Russian often uses a prefixed verb.