nebousita seide, sihatu ni noriokuremasita.

せいで means something like because of..., but it usually carries a negative, unfortunate, or sometimes blaming nuance.

So in this sentence, 寝坊したせいで means:

• because I overslept
• due to oversleeping
• as a result of oversleeping

with the feeling that oversleeping caused a bad outcome.

This is different from a more neutral ので or から.

• 寝坊したので、始発に乗り遅れました。
  = A neutral Because I overslept, I missed the first train.

• 寝坊したせいで、始発に乗り遅れました。
  = Because I overslept (and that caused a problem), I missed the first train.

Because せい connects to the plain form of a clause, not the て-form.

So the pattern is:

• verb (plain form) + せいで
• い-adjective + せいで
• noun + の + せいで
• な-adjective + な + せいで

Examples:

• 雨が降ったせいで、試合が中止になった。
• 風邪のせいで、学校を休んだ。
• 静かなせいで、逆に落ち着かない。

Here, 寝坊した is the plain past form of 寝坊する, so 寝坊したせいで is correct.

This is very normal in Japanese.

Inside a sentence, clauses that modify or connect to other parts often use the plain form, even when the final verb is polite.

So:

• 寝坊したせいで = subordinate clause in plain form
• 乗り遅れました = final main verb in polite form

This kind of mix is standard Japanese, not a mismatch.

You will see this all the time:

• 昨日見た映画はおもしろかったです。
• 時間がなかったので、行けませんでした。

寝坊する means to oversleep or to sleep in too much and end up late.

So 寝坊した is the past tense:

• I overslept
• I slept in

It usually implies that oversleeping caused some kind of problem, especially lateness.

This is a little different from just saying:

• よく寝た = I slept well / I slept a lot

寝坊した strongly suggests I slept longer than I should have.

始発 means the first departure of the day, especially for a train, subway, or bus.

In this sentence, it most naturally means:

• the first train
• the first train of the day

You may also hear:

• 始発電車 = first train
• 始発のバス = first bus

In everyday Japanese, just 始発 is often enough when the context makes the type of transportation clear.

In 始発に乗り遅れました, the particle に marks the thing/event that someone was too late for.

The key expression is:

• 〜に乗り遅れる = to miss ~ by being late to board it

So:

• 電車に乗り遅れる = miss the train
• バスに乗り遅れる = miss the bus
• 始発に乗り遅れる = miss the first train

This に is part of the pattern used with 乗り遅れる.

乗り遅れる means to miss a train/bus/etc. because you were too late to get on.

It is built from:

• 乗る = to ride / get on
• 遅れる = to be late

So literally it is something like:

• to be late for boarding

That is why it does not just mean a general miss in every sense. It is specifically used for transportation or things you board.

Examples:

• 電車に乗り遅れた。 = I missed the train.
• バスに乗り遅れそう。 = I might miss the bus.

Both can sometimes be translated as miss, but they are used differently.

• 乗り遅れる = miss transportation because you were late getting on
• 逃す = miss an opportunity/chance, let something slip away, fail to catch something

Examples:

• 電車に乗り遅れた。
  = I missed the train.

• チャンスを逃した。
  = I missed the chance.

You would normally use 乗り遅れる for trains, buses, and similar things, rather than 逃す.

No, it is not strictly necessary.

You can write:

• 寝坊したせいで、始発に乗り遅れました。
• 寝坊したせいで始発に乗り遅れました。

Both are fine.

The comma just makes the pause clearer and can improve readability. In short sentences, it is often optional.

Yes, grammatically you can, but the nuance changes.

• 寝坊したので、始発に乗り遅れました。
  Neutral, factual.

• 寝坊したから、始発に乗り遅れました。
  Also because, a little more conversational/direct.

• 寝坊したせいで、始発に乗り遅れました。
  Emphasizes that oversleeping led to an unfortunate result.

So せいで is the best choice if you want to highlight the bad consequence.

Yes. It does not always mean blaming someone else. It can also be used for:

• your own mistake
• someone else’s fault
• bad circumstances
• an unfortunate cause

In this sentence, the speaker is basically saying:

• Because I overslept, I missed the first train.

There is a slight self-blaming or regretful tone, which fits せいで very well.

Japanese often leaves out subjects when they are obvious from context.

So this sentence does not need 私:

• 寝坊したせいで、始発に乗り遅れました。

It naturally implies something like:

• I missed the first train because I overslept.

If you added 私, it would usually only be for emphasis or contrast.

Yes. Some natural alternatives are:

• 寝坊したので、始発に乗り遅れました。
  More neutral.

• 寝坊して、始発に乗り遅れました。
  Simple and straightforward: I overslept and missed the first train.

• 始発に乗り遅れたのは、寝坊したせいです。
  = The reason I missed the first train is that I overslept.

The original sentence is natural and emphasizes the negative result most clearly.